Can The Father Sign Over Rights Without My Consent

I am 31 weeks pregnant, the first day I learned I was pregnant I told the father of my child. He said he will pay half on abortion I personally don't believe in abortion so that wasn't a option for me. He told me if I didn't have an abortion he would have nothing to do with me or the baby. And would sign over all rights so he wouldn't have to pay for child support. Can he do that without my consent and if so would he still have to pay child support being that he did help make the baby. And how would I go about collecting child support would that case have to get started after giving birth or is there a way to get it started before hand.