I'm currently pregnant and having a hard time with the baby's father.he lives in america and I live in england.im planning on splitting up with him and disappearing with the baby.does he have any rights to find me once the child is born?

Yes, in either nation he will have the right to have visits with the child, and in fact if you try to hide and not allow him to see the child, he may have a good chance at getting custody and taking the child away from you