[I'm putting back an updated version of my removed posting, as I've found more information on this family.]
The Scots immigrant John1 Borland of Boston (husband of Sarah Neal), may have remote royal ancestry through his Baillie or Hamilton lines.
Josephine C. Frost, _Ancestors of Henry Rogers Winthrop and his wife, Alice Woodward Babcock_ (1927), gives:
2. JOHN BORLAND, son of John and Marion (Mack) Borland, was born in Bangor, Ireland, Dec. 23, 1633, and married Mch. 5, 1657, Beatrix (daughter of James Baillie), who at Isle of Eelin in Larn [? Lanark], died about 1674. Issue: John, John, Francis, Janet, Anna.
3. JOHN BORLAND, son of John and Beatrix (Baillie) Borland, was born Feb. 3, 1659, and became a prominent merchant of Boston, Mass., making his will there in 1726 and dying March 30, 1727. He mentions his wife Sarah; only son Francis; three nieces, Cecil, Anna and Euphamie, daughter[s] of his brother Francis Borland, late of Glasford, in North Britain, clerk; ...
End of Quote.
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The brother, Rev. Mr. Francis Borland of Lanarkshire, Scotland, left a surviving diary, now housed at the University of Edinburgh, which has been studied in detail by Jack Ramsay ("The Borland Memorial," _Journal of Presbyterian History_, 41 [1963]: 141-64).
Per this diary of Rev. Francis Borland, the family was in Ireland only briefly in the late 1650s, living most of the rest of the time at Hamilton, Lanarkshire, Scotland. Francis also mentions his brother John, "who was bred a Merchant ... & traded to New England about the year 1680, where afterwards providence did cast his lot in Boston of New England. Here the Lord did order for him a prudent and virtuous wife Sarah Neal, whom he married in [sic] October 23, 1683 by whom he hath several children" (Ramsay, p. 145, footnote 22). The mother of John and Francis is named by Francis as "Beautrice Boulie born about 1624, married March 5, 1657," who was a daughter of "James Boulie Laird of Park in Blantyne Parish and Katherin Hamilton daughter of the Laird of Edstou in Hamilton Parish" (p. 43, footnote 6).
Elsewhere, Rev. Francis Borland mentioned "boarding with my Aunt Janet Bailie," so it's unclear why the name "Boulie" was employed in the details about his mother, unless Ramsey had some difficulties with the handwriting at that point in the manuscript (perhaps the surname was capitalized in that passage ?).
The marriage of John Borland and Beatrice is in the extracted IGI (batch M11647-2), at Hamilton, Lanarkshire, on 28 January 1657 (not 5
March), their names given as "Johne Borland" and "Bitrix Bailzie." Bailzie is a more common variant of Baillie.
Beatrice Baillie's parents are apparently the ones found in this complaint to the Privy Council in 1630:
"Complaint by Katharine Hamiltoun, spouse to James Baillie of Parke, as follows:---On 18th February last she obtained decreit before their
Lordships ordaining her said husband to infeft her in a legal way in the half of his living of Parke, Auchintibber and Corsbasket, with the
burden of the entertainment of their three daughters and payment of the annual rent of 1000 merks. He has not obeyed the decreet and has been put to the horn accordingly and comtemptuously remains thereat ..." (P. Hume Brown, ed. _The Register of the Privy Council of
Scotland_, 2nd series, vol. 4, pp. 95-96 [extensive petition by Katherine Hamiltoun]).
End of Quote.
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http://books.google.com/books?id=EcYvAAAAMAAJ&pg=PA95&dq=%22entertainment+of+their+three%22&hl=en&sa=X&ei=n-aXUdmbMvPG4APeioGAAQ&sqi=2&ved=0CC0Q6AEwAA#v=onepage&q=%22entertainment%20of%20their%20three%22&f=false
James Baillie has a known mistress, Jean Henderson of Parke, and Katherine Hamilton accused both of them to the Council the following year, 1631, "the complainer appearing by her brother, James Hamilton of Barncluthe ..." (p. 114).
https://www.google.com/books/edition/The_Register_of_the_Privy_Council_of_Sco/EcYvAAAAMAAJ?hl=en&gbpv=1&dq=barncluthe&pg=PA748&printsec=frontcover
Sir James Balfour Paul, _The Scots Peerage_, 2:41-42, shows that James Hamilton "of Barncleuch" had a sister "Catherine, married to Baillie of Park"; these two were children of John Hamilton of Udston, parish of Hamilton, and his spouse Margaret Muirhead of Lachop. Compare the place name of Udston, Hamilton parish, with Francis Borland's statement about his great-grandfather Hamilton "of _Edstou_ in Hamilton Parish" (I suspect what Francis really wrote was "Edston," close enough to Udston.)
Rev. Francis Borland mentions being educated at Glasgow in the 1670s in some fashion by "Mr. Francis Kincaid, my uncle in law" (Ramsey, p. 143).
The following records, drawn from the IGI, show a Francis Kincaid with wife Margaret Baillie and numerous family at Hamilton and nearby Glasgow.
Hamilton, Scotland, baptisms of children of Francis Kincaid with no wife named:
--Christian Kincaid, dau., bapt. 1647
--William Kincaid, son, bapt. 1649
Glasgow, Scotland, records of Kincaids, all baptisms showing the mother's family name ("Baillie"):
--George Kincaid, son Francis & Margaret, bapt. 1652
--Margaret Kincaid, who married in 1653 to Matthew Cumming
--Matthew Kincaid, son Francis & Margaret, bapt. 1653
--Sarah Kincaid, dau. Francis & Margaret, bapt. 1655
--Janet Kincaid, dau. Francis & Margaret, bapt. 1656
--Francis Kincaid, son Francis & Margaret, bapt. 1658
--Jean Kincaid, dau. Francis & Margaret, bapt. 1660
This Kincaid-Baillie family is central in a complex legal dispute between Kincaid, Cumming and Scot, over the lands of John Baillie of Parke and Corsebasket, apparently a brother of Beatrix Baillie, wife of John Borland (though no Borlands are found in the dispute) [see Brown's _Supplement to the Dictionary of the Decisions of the Court of Session_ 4: 515-16]:
December 24, 1701. I reported the competition about the estate of Mr John Kincaid of Corsebasket, advocate, betwixt Matthew Cumming and Margaret Scot, his sister's children, and his nearest of kin. John Baillie of Park, heritor of the lands of Corsebasket, makes a tailzie of these lands in 1659, to himself and the heirs of his own body; whilk failing, to John Kincaid his nephew, and the heirs of his body; then to Francis Kincaid and his heirs, and, last of all, to Margaret Kincaid their sister, and the heirs of her body. After Baillie's decease, John Kincaid does not prosecute the tailzie, but charges Baillie's sisters, as heirs of line, to enter heir to him in the said lands of Corsebasket; which they accordingly did, and disponed to him these lands, but exactly in the terms of their brother's tailzie, whereupon John is infeft; but afterwards resolving to change the holding, he resigns in the hands of the Duchess of Hamilton, superior, and prevails with her Grace to get them changed from ward to feu; and in this charter the tailzie is neglected, and the lands taken to himself, and the heirs of his own body; which failing, to his brother Francis, and the heirs of his body; and these also failing, the fee to return to himself, and his own heirs whatsomever; and on this he is also infeft. On John Kincaid's decease in June 1700, Matthew Cumming, eldest son to Margaret Kincaid, the last branch and member of the tailzie made by John Baillie, serves himself heir of provision and tailzie to the said John Baillie, and thereon infefts himself as _haeres ex asse_ in the whole lands; Margaret Scot, a niece of John Kincaid's by another sister, retours herself heir portioner to her uncle, and being also infeft, pursues, etc. etc. ...
End of Quote.
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https://www.google.com/books/edition/Supplement_to_the_Dictionary_of_the_Deci/r6xKAQAAIAAJ?hl=en&gbpv=1&dq=%22betwixt+matthew+cumming%22&pg=PA515&printsec=frontcover
The only baptisms of persons named immediately above which I can't find are those of Francis and Margaret Kincaid's two elder children John Kincaid and Margaret Kincaid; but the Cumming marriage of Margaret Kincaid is in the Glasgow records along with the baptisms of her younger siblings.