We are Mayflower descendants. For sure.

After many decades of the story being told in my family that we were descendants from the Mayflower passengers, I have found the source material to prove it.

However according to our family stories, it was suppose to be the Morrill line, and I have run across much web site information and chronicles stating such, however I have not seen proof.

This is the direct line I have proof of ... the South family line, my father’s mother's mother family. Edward Fuller’s son Samuel’s daughter Hannah married Nicholas Bonham and their daughter Hannah married Daniel Lippington whose daughter Dorothy married Thomas South, my 7th great-grandfather.

Edward Fuller - Mayflower Passenger
Relationship to Michael Tieman: 11th Great-grandfather
Born: 4 Sep 1575, Redenhall, England
Died: 11 Jan 1620, Plymouth Colony, Massachusetts

Edward Fuller has been generally identified as the son of Robert and Sara (Dunkhorn) Fuller, baptized on 4 September 1575 at Redenhall, Norfolk. Thomas Morton, writing in 1637, says that Samuel Fuller (brother of Edward Fuller) was the son of a butcher. The name Matthew also occurs in this Redenhall Fuller family.
     The name of Edward Fuller's wife has not been discovered. In James Savage's Genealogical Dictionary of the First Settlers of New England (1860-1862), Edward Fuller's wife was given as "Ann". However, there are no American or English records which give her name. I suspect James Savage may have made a simple typographical error: Mayflower passenger Edward Tilley had a wife Ann; or perhaps he was thinking of their sister Ann Fuller. Nonetheless, numerous sources published after 1860 have utilized Savage's Genealogical Dictionary, and so the identification of Ann can be found in numerous other books and online resources.
     Very little is known about Edward Fuller. What is known is that he, his wife, and his son Samuel came on the Mayflower in 1620 to Plymouth. A single Leiden judicial document mentions Edward Fuller, and proves that he, like brother Samuel Fuller, were living in Leiden. As stated by Governor Bradford, "Edward Fuller and his wife died soon after they came on shore." Edward died at Plymouth, between January 11 and April 10, 1621; his wife, whose name is sometimes given as Ann, but is really wholly unknown, died early in 1621, after January 11th. but son Samuel (who would have been about 12), survived. An older brother, Matthew, had stayed behind and came to America in 1640.
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Samuel Fuller - Mayflower Passenger
Relationship to Michael Tieman: 10th Great-grandfather
Born: About 1608, Redenhall, England
Died: 31 Oct 1683, Barnstable, Massachusetts
Occupation: At age 12 arrived in America on Mayflower

Samuel Fuller, (Edward'), b. about 1608, at some place in England not yet found, no record of his birth or baptism having been discovered; d. Oct . 31,-Nov. 10, 1683, at Barnstable, Mass.; m. at Mr. Cudworth's house in Scituate by Capt. Miles Standish, magistrate, "on ye fourthe day*e of ye weeke", April 8-18, 1635, Jane Lathrop, dau. of Rev. John Lathrep of Scituate and (after 1639) Barnstable, bapt. Sept. 29, 1614, at Edgerry, Co. of Kent, England; d. subsequent to 1658 and before 1683, but the exact date is not found.
     Samuel Fuller grew up under the care of his uncle, Dr. Samuel Fuller, at Plymouth. He had three acres at the division of lands in 1623, receiving, it is thought, those of h1s father and mother, and one for himself. If this theory is correct he was at least sixteen years of age at the time, and his birth occurred as early as 16o8, instead of 1612 as we have conjectured above. It is not quite certain however that he was old enough to work this land alone.
     Gov. Bradford's words about this matter are as follows: " All this while no supply was heard of, neither knew they when they might expecte any. So they begane to thinke how they might raise as much come as they could, and obtaine a beter crope than they had done, that they might not still languish in miserie. At length, after much debate of things, the Gov (with y« advise of y« cheefest among them) gave way that they should set corne every man for his owne perticuler, and in that regard trust to themselves ; in all other things to goe on in y* general way (as a joint-stock company) as before. And so assigned to every family a parcell of land, according to the proportion of their number for that end, only for present use (but made no devission for inheritance), and ranged all boys and youth under some familie. This had very good success." Bradford's History of " Plimouth Plantation", ed. Mass. p. 162.
    The land assigned to him was on the South side of the town brook; " to the Woodward" and included what is now Watson's Hill. His neighbors were John Howland, Stephen Hopkins, Edward Winslow (?) Gilbert Winslow, and the Indian Hobomok.
     On June 1, 1627 at a town-meeting, the inhabitants were divided into twelve groups for the purpose of dividing the cattle then owned in the Colony. " The eighth lot fell to Samuel Fuller (the Doctor) . and his company ; joined to him his wife Bridget Fuller, Samuel Fuller, Jr., Peter Browne, Martha Browne, Mary Browne, John Ford, Martha Ford, Anthony Annable, Jane Annable, Sarah Annable, Hannah Annable, Damans -Hopkins. To this lot fell a red heifer, came of the cow which belongeth to the poor of the Colony, and is of that consideration, viz.: these persons nominated to have half the increase; the other half with the old stock, to remain for the use of the poor."
     He is mentioned in his uncle's will in 1633 as follows: " It. my will is that my Cozen (nephew) Samuell goe freely away with his stock of Cattle and Swine without any further recconing w«* swine are the halfe of six sowes, six hogges, one boare & four shotes. Also one Cow & one heyfer." " It . my will is that in case my sonne Samyell and other my children die before such time as they are fit to enter upon my land for inheritance that then my kinsman Sam. ffuller now in the howse with me enjoy w1soever lands I am now possessed of except my dwelling howse at town or whatsoever shall be due to me or them." " It. I give to him my Rufflet Cloake c my stuffe sute I now weare." The date of this will is July 3o, 1633 and within three months of that date the good doctor had been laid to rest.   
    As the doctor's children survived, Samuel' received none of the lands, and soon, apparently, started out with the cattle and wine to seek a home. The whole transaction seems clearly to show that he had reached man's estate, being at least 21, and perhaps as much as 25 years of age at the time.
    He became a freeman of the Colony in 1634, and settled in the nearby town of Scituate, where on April 8-18, 1635, as before stated, he married Jane, daughter of Rev. John Lathrop, the pastor of the Scituate church. Nov. 7, 1636 he joined the church of Scituate, having a letter of dismission from the church of Plymouth, of which he had been a member. He built in 1636 the fifteenth house in Scituate, on Greenfield Street, the first lot abutting on Kent Street. He had twenty acres of land on the east of Bellhouse Neck in that town, probably a grant from the town.
    The kind of house these early settlers built is worthy of note. Mr. Lathrop calls them " small plaine pallizadse Houses." The walls were made of poles filled between with stones and clay, the roof thatched, the chimney to the mantle of rough stone, and above of cob-work, the windows of oiled paper, and the floors of hand sawed plank*. Mr. Lathrop who had been accustomed to life in Christ's College, Cambridge, and to a generous life in England, truly says that the dwellings in Scituate were " meane ". Elsewhere he calls these structures booths, and says they were open and cold, and in winter a high piled fire had constantly to be kept burning. All the houses in the village were alike,— there was no opening for pride to claim supremacy.
    In June and July 1639 the Rev. Mr. Lathrop and many of the members of his church removed and founded the town of Barnstable, probably at the time the most easterly settlement on Cape Cod. If Samuel Fuller and his young family did not at once follow him thither, he did so in a few years. Otis, following the church records of Barnstable, thinks that he was there as early as 1641, basing his view on the fact that the Barnstable church record contains the baptism of his daughter Sarah on August 1, 1641, and of Mary on June 16, 1644. Otis says further that it does not appear that he was an inhabitant of the town till after January first, 1644. Now it is quite possible that the baptismal record is correct, and that Samuel Fuller did not settle in Barnstable until 1650. There being no pastor at Scituate, it is quite likely that the two children were carried to Barnstable, or that the Rev. Mr. Lathrop visited Scituate, for their baptism. The record was little more than the minister's private diary, and all that it can certify to is the fact the children were baptized by him. The place might be anywhere he might be, if not within the parish of another settled pastor. The reasons for thinking that Samuel Fuller settled in Barnstable as late as 1650 are two.
     In the second volume of Plymouth Colony deeds, folio 1. ( See Mayflower Descendant, Vol. 1. April 1899, p. 91) is a deed which begins as follows: " To all Christian people to whom this p'sent writing shall com Samuel Fuller of Scituate in the government of New Plymouth in New England in america sendeth greeting:" He then proceeds to convey to " Peter Collymore of Scittuate " " one dwelling house and a barne and Cowhouse with sixteene acars of upland more or less bounded on the west with the land of Mr William Varssall, on the south with the land of Resolved White, on the north with the hieway by the herring brook; and on the last with the mersh; as allsoe two pcells of mersh land contoining twelve acars, with all and severall the appurtenances thereunto belonging or any way apperteining." This deed was signed and sealed March 25, 1650, the first day of the year according to the calendar then in use, equivalent to April 4, 1650, N. S.
    Samuel Fuller signed his name to this deed and there is appended the consent of his wife, as follows: "The 16th (26th N. S.) of May 165o Jane Fuller the wife of Samyel Fuller did com before mee Timothy Hatherley asistant to the Governor of New Plym : in New England and did freely acknowlidg her willingness of the within Mencioned sale and did freely Resigne up her Right to Peeter witnesses Collymore. Timothy Hatherley.
     This is perhaps the only mention to be found of Samuel Fuller's wife Jane after her marriage. Mr. Hatherley was never a resident of Barnstable, and everything seems to show that the Fullers were still in Scituate at this date, May 16-26, 165o.
     The other reason is that the first recorded birth of Samuel's children occurs on the Barnstable records, in the birth of the child Thomas on May 18, 1651. The earliest records of Scituate are lost.
Captain Matthew Fuller, Samuel's cousin, appears to have removed from Plymouth at about the same time, and together they bought of Secunke, an Indian, Scorton or Sandy Neck, that is, so much of it as lies within the town of Barnstable. The arable land in the purchase was set off to the Fullers, the remainder, including the meadows, was reserved as town commons, and afterward divided.
     Samuel Fuller also bought meadow of his cousin Matthew that was Major John Freeman's and meadow of Samuel House, and land on Scorton Hill. He lived in the northwest angle of the town in a secluded spot, where few had occasion to pass. He had been a constable at Scituate in 1641, and his name appears a few times as juryman, or committee to settle difficulties with the Indians.
    He was the only one of the passengers of the Mayflower who settled permanently at Barnstable, and one of the late survivors of that immortal company. He was buried, if not on his own estate, in the ancient burial place at Lothrop's Hill in Barnstable, near the site of the first Meeting House. No gravestone now exists."

Genealogical and Family History of Western New York, Volume 2 edited by William Richard Cutter