My mother's DNA (Ancestry.com) shows a connection to two others (dicqs and pnhyde) with Peckham forbears in Hordle and Sopley in Hampshire. My mother's paper trail genealogy clearly shows that she is descended from Aaron Peckham the Second Fleet convict and Sarah Chapman. The Hampshire Genealogical Society baptismal transcripts show that an Aaron Peckam (note spelling of the surname) was born 1765 and baptised at Eling, Hampshire on 9th December 1765. His mother's name is given as Susannah (no surname listed but presumably Peckam?) and there is no father's name listed. Aaron is listed as “baseborn”. This would explain the aliases recorded in the convict records (Cock, Cook, Peckham).
The Hampshire Genealogical Society marriage transcripts record that an Aaron Peckam married a Mary Hatch at Eling, Hampshire on 30th November 1785 (also recorded in Phillimore's marriage register). I note that Aaron was charged with stealing a horse in 1787 from a William Hatch of Eling who may have been his father in-law. I also note that a Susana Peckam died 1787 at Minstead, Hampshire (Hampshire Genealogical Society transcripts). I wonder if Aaron stole his father in-laws's horse to visit his dying mother? It seems plausible.
I further note that the Peckham forbears of dicqs and pnhyde could be Royall Peckam 1718-92 of Minstead, Hampshire and his wife Susannah nee Knowlton 1728-87. I further note that various rarer names (Angell, Royall, Knowlton etc) associated with the Royall Peckham family occur in my mother's DNA matches in statistically anomalous numbers, which suggests that my mother's forbears include persons with these surnames. In other words, there is a high probability that Aaron Peckham is related by blood to Royall Peckham. The name Knowlton (Royall's wife's maiden name) occurs ten times in my mother's DNA matches whereas statistically it should show up with a probability of 3.85. The Poisson probability of this happening by random is 0.6%. Similarly, other names associated with the Royall Peckham genealogy occur with statistically anomalous numbers in my mother's DNA matches. ie. Angell occurs eleven times whereas the expected frequency is 3.27. Royall occurs seven times whereas the expected frequency is 3.2.