FULLER: Genealogy of some descendants of Edward Fuller of the Mayflower 1908By William Hyslop Fuller This is the Fuller family genealogy, showing the record and descendants of Edward Fuller who came to America on the Mayflower in 1620. He was a Puritan who left England due to religious persecution. In the time of Queen Elizabeth 1558 to 1603 the policy was to enforce absolute uniformity in religious belief. King James l, who succeeded her was also intolerant in religious matters. Several Fullers came from England to America