His baptism shows that he was indeed illegitimate:
Abraham Pellunt bp.20/7/1828 Abbey, St. Albans, son of Mary Pellunt.
His father may indeed have been a William but not a Pallent and I would think it impossible to ever find out who he was. He was clearly conceived back in Hertfordshire.
As to his mother Mary Smith bc.1795/6 St. Albans.
I note when she married Robert Pallent that one of the witnesses was a Sarah Smith - probably either a sister or her mother.
IGI shows a Mary Smith bp.29/3/1795 St. Stephens, St. Albans, dau. of a John and Sarah and also a sibling Sarah Smith bp.13/3/1791 which could be them.
Annette