General Society of Mayflower Descendants has announced the discovery and published the ancestry of Mayflower passenger William White in 2017. All sources before this date are likely to be incorrect.
The origins of Mayflower passenger WIlliam White have recently been discovered and published in 2017. This article from The American Genealogist supersedes and replaces all previous work and speculation regarding his birth, parents and marriage. 
The origins of William White have long been sought and discussed in the genealogical literature. Noted Mayflower historian Caleb Johnson has recently shown that he was William White, son of Edward White and Thomasine Cross, baptized in Wisbech, Cambridgeshire. Because of the numerous previous articles and books which have been written about William White, care must be taken not to rely on out-of-date information. Specifically:
The identification was made based on the discovery of his baptism, and the numerous family connections of this White family with other members of the puritan community in Amsterdam. He was the half-brother of Henry May who was the father of Dorothy May, wife of Governor William Bradford. He witnessed the marriage of his half-sister Jacomine May in 1609 in Amsterdam. This William White also had a first cousin named Peregrin, a very distinctive name which he gave to his own child, Peregrine White.
Baptized: 25 January 1586/7 in Wisbech, Cambridgeshire, England.  He was the son of Edward White and Thomasine Cross.
Marriage and Children
Married: Susanna Jackson about 1614 (estimate based on the birth of first child). They traveled on the Mayflower with their son Resolved. Their second son Peregrine was born while the Mayflower was offshore (before disembarking). William died the first winter. She was the daughter of Richard Jackson and Mary Pettinger.
She married 2nd Edward Winslow on 12 May 1621 at Plymouth (the first marriage at Plymouth) by whom she had five children.
Children of William White and Susanna Jackson: 
Resolved White. Born about 1615 (deposed aged 59 in 1674 and aged 63 in 1678).
Peregrine White. Born 4 December 1620 ("Whilst some were employed in this discovery [of a good harbor], it pleased God that Mistress White was brought abed of a son, which was called Peregrine" (Mourt, 31).
Children of Edward Winslow and Susanna Jackson:
Unnamed child who died young.
Died: 21 February 1620/1 at Plymouth Colony, New England. 
William White was among those who died during the first winter in New England.
Most likely he was buried on Coles Hill, Plymouth in an unmarked grave as was the custom at that time - so the Indians could not tell that the Pilgrim ranks had become so decimated. William White's name appears on the Pilgrim Memorial Tomb located on Coles Hill. (The Tomb contains only a small sampling of unknown remains found in the Plymouth vicinity long ago but are not identified as those of any Pilgrims. 
The May and the White families, both from Wisbech, Cambridgeshire, arrived in the Netherlands around 1608. The marriage of Gov. William Bradford to Dorothy May in 1613 states that she was 16 years old and that she had been living there for about 5 years. Henry May the Elder stated in 1627 that he had been living in Amsterdam for about 15 years. In June 1608, "Willem Wit" was granted permission to reside within the city, and in August 1608 "Hendrick May" also received permission. In 1611, William White purchased a house in the "new city" of Amsterdam.
William White was a member of Henry Ainsworth's congregation of Separatists in Amsterdam. His half-brother, Henry May was a leading elder of this congregation.
Mayflower in Plymouth Harbor by William Halsall, 1882.
After a couple of false starts the Mayflower left Plymouth, England on 6 September 1620 for what was originally planned to be a journey to Virginia. Onboard were 102 passengers, including this William White. The historic voyage took 66 days, and on 9 November 1620, the Mayflower arrived at Cape Cod (well off-course). A decision was made, however, to remain at Cape Cod for safety rather than attempt to sail south to the area they were supposed to settle by the terms of their patent.
Signing the Mayflower Compact 1620, by Jean Leon Gerome Ferris, 1899.
Immediately upon arrival some dissension broke out among the colonists. Since they were not settling in the area specified by their patent, some colonists felt they were no longer bound by the laws of England and the terms of the patent. An agreement was drawn up to help establish law, government and social order. The Mayflower Compact was signed while the Mayflower was anchored at Cape Cod (Provincetown Harbor) on 11 November 1620. It was signed by all free adult males and some, but not all, of the servants. William White was the eleventh male to sign.
In his list of those who came in the Mayflower Bradford includes "Mr. William White and Susanna his wife and one son called Resolved, and one born a-shipboard called Peregrine, and two servants named William Holbeck and Edward Thompson" (Bradford, 442). In his accounting of 1651 Bradford tells us that "Mr. White and his two servants died soon after their landing. His wife married with Mr. Winslow, as is before noted. His two sons are married and Resolved hath five children, Peregrine two, all living. So their increase are seven" (Bradford, 445).
After their arrival in America, the Pilgrims spent the first month exploring and eventually settled on an area for their new colony which they would name Plymouth. However, because of the winter conditions, the new colonists only managed to build one building in the first winter. Most of the colony continued to live aboard the Mayflower for months after their arrival.
The harsh conditions with disease, inadequate shelter, and scarce resources led to a very high death rate during the first year. Forty-five of the 102 passengers died the first winter, including William White and both of his servants, William Holbeck and Edward Tompson. Three other Mayflower passengers died on the same day as William White.
In the 1623 Plymouth division of land William White received five acres as a passenger on the Mayflower (even though he had been dead for two years) (Plymouth Court Records, 12:4]. In the 1627 Plymouth division of cattle Resolved White and Peregrine White were the tenth and eleventh persons in the third company (Plymouth Court Records, 12:10).
Common Errors to Avoid
Origin Forgery: The supposed bible of William White has been mentioned in a G2G thread and on the page of his wife. This bible was 'discovered' in the 1890s and published in various forms over the next decade.  It has long since been proved a forgery, and should not be referred to in any discussion regarding William and Susanna White. 
Incorrect parents: : Robert M. and Ruth W. Sherman have suggested that William White may have been a nephew of Alexander and Eleanor White of Sturton-le-Steeple in Nottinghamshire, England. Bishop John White of Barham, Suffolk, did not mention a son William in his will, nor any son "who left his country and his church" (Mayflower Quarterly, 41:16-18). This is now shown to have been wrong.
LNAB of wife: His wife has recently been identified as Susanna Jackson, daughter of Richard and Mary (Pettinger) Jackson. She was not Susanna Fuller as was long speculated. Please her page for further details.
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Footnotes and citations:
↑ 1.01.11.21.31.4 The American Genealogist, vol. 89 no. 2 (April 2017): 81-94.
↑ 2.02.12.22.3 The American Genealogist, vol. 89 no. 3 (July 2017): 168-188.
↑ Website: Tales from the Vault: Our Mayflower Bible, by John B. Thomas III (2001, accessed July 2016)
The American Genealogist Whole No. 355 Vol. 89 No. 3 July 2017 p. 180
The American Genealogist, vol. 89 no. 2 (April 2017):81-94. The English Origin and Kinship of Mayflower Passengers William1 White and Dorothy1 (May) Bradford of Wisbech, Cambridgeshire, by Caleb Johnson, Sue Allen, and Simon Neal.
The American Genealogist, vol. 89 no. 3 (July 2017):168-188. The English Origin and Kinship of Mayflower Passengers William1 White and Dorothy1 (May) Bradford of Wisbech, Cambridgeshire (cont.), by Caleb Johnson, Sue Allen, and Simon Neal.
The American Genealogist Whole Number 356 October 2017 Vol. 89 No. 4 "The origin of Mayflower passenger Susanna (Jackson) (White) Winslow" p. 241-264.
Anderson, Robert Charles, The Great Migration Begins: Immigrants to New England, 1620-1633, vol. III, P-W. (Boston: NEHGS, 1995):1980-1981, biography of William White. American Ancestors.org LINK
Caleb Johnson's MayflowerHistory.com Website. Biography of William White.
I seperated Ann(a) Fuller now from this William White, I wanted to create a new William White Profile for Anna as requested in the G2G about the controversy, but there already was one, and he was attached to a duplicate Susanna Unknown + there also was again a duplicate of Edward Winslow, she was attached to..
Merged the Duplicate Susanna Unknowns now and will work on things to make sure it all is correct again and as requested in this G2G
Have you seen and read the marriage record of Samuel Fuller already ?
I am looking at this Mayflower History.com Because this is what seems to be the only reason for this confusion ?
1. Samuel Lee , there is nothing about William White present at any event after the Mayflower left see: records Samuel Lee Leiden archive and see the record from april 1621 No William White was present here at all, so leaves only this : And since Sarah Priest had witnessed the will of William White in 1612, wouldn't it be reasonable to assume it was the same William White who witnessed her own marriage to Godbert Godbertson in Leiden in October 1621 ?
So I will try if I can find that marriage as well , since it is mentioned William was present there as well ??
Maybe someone was confusing this : Thybault, Willem Cornelisz. for William White ?
Bea, read g2g post associated with wife Susannah. The William White who married Ann Fuller in Leiden was NOT the Mayflower man. The 1612 marriage information on this page refers to a different William White, wool comber, who was still in Leiden a year after the Mayflower landed in Plymouth. It needs to be removed from this profile.
I know there was done a lot of research for them already, but it is all quite confusing now , this source says this Susanna Fuller and her husband were passengers of the Mayflower, there was just one William White with his wife Susanna White at the passenger list ?
William White is mentioned as brother in law of Samuel Fuller in a different record and I am still searching for the mentioned second William White from England, but did not find him yet. So is it ok to look for more sources or ?
I'm trying to find the son Resolved as well and as you can see the records are not that easy to read so it might take a while to find him, if there is a record of the baptism at this archive that is of course...