Facts and Events
Caleb Johnson found the origins of Peter and his brother John in Dorking, Surrey. They were sons of William Browne, and had several associations with the Mullins family, who also came on the Mayflower. The family of Family:Thomas Browne and Joan Gabb (1) has been discredited as his parents.
Life in Plymouth, MA
Peter Browne arrived at what was to become Plymouth, MA, aboard the Mayflower.
On 12 January 1621, Peter Browne and John Goodman had been cutting thatch for house roofing all morning. They ate some meat and went for a short walk to refresh themselves, when their two dogs (an English mastiff and a English spaniel) spied a great deer and gave chance. Peter and John followed and quickly got lost. They wandered around the entire afternoon in the rain, and spent the night in a tree (and pacing back and forth under it) fearing that they had heard lions roaring in the woods. The next day they made their way up a hill, spotted the Bay, reoriented themselves, and made it back home to an extremely worried Colony that had already sent out two exploring parties in an attempt to find them.
In 1623 Plymouth land division "Peter Browen" received one acre as a passenger on the Mayflower.  By about 1626, he married widow Martha Ford, the only single female who arrived on the Fortune in 1621 (her husband had died en route). In 1627 Plymouth cattle division Peter Brown, Martha Brown and Mary Brown were the fourth, fifth and sixth persons in the eighth company. 
On 11 November 1633 a court of assistants at Plymouth ordered that "whereas Peter Browne died without will, having diverse children by diverse wives, his estate amounting to an hundred pounds, or thereabouts, it is ordered, that Mary, his wife, who is allowed the administra~trix of the said Peter, forthwith pay down fifteen pounds for the use of Mary Browne, daughter of the said Peter, to Mr. Joh. Done, of Plymoth aforesaid, with whom the said Court have placed the said Mary for nine years; at the end whereof the said John is to make good the said fifteen pounds to her or her heirs, if in case she die. Also it is further ordered, that the said widow Mary Browne pay or cause to be paid into the hands of Mr. Will[iam] Gilson the full sum of fifteen pounds, for the use of Prisilla Browne, another of the daughters of the said Peter, the Court having placed the said Prisilla with the said Will[iam] for 12 years, at the end whereof the said Will[iam] is to make good the same unto her, as her father's legacy as aforesaid; & to that end the said John & Will[iam] either stand bound for other for performance of the several payments, as also for such other performances of meat, drink, clothing, &c., during the said term, as is meet.
"And for the rest of the estate, the widow having two children by the said Peter, together with her own 3d, it is allowed her for bringing up the said children, provided that she discharge whatsoever debts shall be proved to be owing by the said Peter, & the legacies given by the Court. For performance whereof she & Mr. Will[iam] Brewster bound in two hundred pounds" .