In Delaware and I believe most other states of his name is not on the birth certificate nothing they can do, bc he has the right to refuse a DNA test. If he signed the bc and signs his rights over they can still make him pay.
@alecialynn, my attorney said that even if my ex didn't want rights the state would still make him pay child support.... he said if not, every dead beat dad would sign rights over.... its their responsibility. He said that unless I was re married, and my new husband "adopted" the child, would my ex be able to file to not pay child support. Not sure where you live, but this was the case where I was.