Concerning the Boleyn-Butler relationship, there has been a rumor for over 500 years that Queen Elizabeth I had a child with her cousin Thomas Butler, 10th Earl of Ormonde. This child was Piers Butler of Duiske, his father's favorite among his legitimate children and at least 12 illegitimate ones.There is anecdotal information , but this is the most interesting link I have found. There are also rumors that Queen Elizabeth was the mother of Sir Francis Bacon and Richard Devereaux, Earl of Essex as well as William Shakespeare!
I am a member of The Butler Society. This is from their scholarly website:
Piers Butler (d, 1601) of Duiske, Co. Kilkenny.
Clue: He was base son of Black Tom, 10th Earl of Ormond (d, 1614), but who was his mother? (per Dame Elizabeth Butler-Sloss, whose husband is an heir-general of this Piers).
Reply: Black Tom (b, c. 1531 and brought up a Protestant at Court) was in England until Nov. 1554. The Virgin Queen (b, 1533) is said to have called him her black husband. In any event, they became lifelong friends, as evidenced in moulded plaster and carven stone by her initials paired with his, the royal arms displayed with those of Butler and her portrait replicated in the motif of the carefully restored frieze, in the house he built at Carrick-on-Suir, Co. Tip; and in 1955 Blake Butler, who was no mean pincernalogist, wrote to me: "the story of their child existed in their lifetime and was repeated to this day (J.R.I.A.S. (1929), 41; Waterford Archaeol Soc., ii, 224; etc.)". This Piers (whose year of death was incorrectly given as 1603 in Carrigan, Ossory, ii, 297) must have been born before 1560 because he was granted a lease (of Duiske) as early as 2 Nov. 1580 (Irish Monastic Deeds, 271). As Blake Butler went on to observe, the extent to which Piers was favoured in his father's Will indicated his mother was someone of great importance; and Blake Butler managed to identify the mother of each of the dozen illegitimate children Black Tom is known to have had, except for two, viz: a daughter, Elles, and this Piers. Towards the end of 1553 the future Queen Elizabeth might have had the opportunity to conceive Piers. In the following Feb. she was said to be pregnant at Ashridge and, having gone to Woodstock, via Windsor, in May 1554, she spurned medical aid, with the brave words, "I am not minded to make any stranger privy to the state of my body, but commit it to God". Finally, after dining, 11 Dec. 1921, with Cora, widow of 9th Earl of Strafford (killed by a train, 1899), the 3rd Lord Oranmore & Browne troubled to note in his well-informed Journal that she then told him that her husband "was in waiting at Windsor when Holmes, the librarian, showed him a little packet of letters he had discovered in the library - they consisted of the charges made by Doctor, Midwife etc. for the confinement of Queen Elizabeth with letters from the Queen directing that the child should be sent to some place in Cornwall to be brought up with her two children, who were all to bear the name of Tudor - Holmes sent these letters to Queen Victoria to see and he told Lord Strafford that a few days afterwards he saw the Queen who told him that she had read the letters with great interest, but as they were of no historical interest (!) it would be better that they should be burnt. Accordingly she made him burn them in her presence" (quoted by kind permission of the present Lord Oranmore & Browne, via John Butler of Rotherfield, Sussex).
My great-grandfather James Butler was born in 1832. about 10 miles away from the 10th Earl's estate at Carrick-on-Suir. The quest for my link continues. Mary
CORRECTION for earlier post: Lady Margaret Butler was the MOTHER of Thomas Boleyn and thus the grandmother of Anne, Mary and George Boleyn. So the 7th Earl of Ormonde was the grandfather of Thomas Boleyn.