If I sign over my parent rights, do I still have to pay child support

Yes. Unless someone else assumes the responsibility.

Yes of course you do, unless the child is being adopted by a step parent who takes over the responsibility. As a parent, you can give up your rights, but not your obligations.

If you could just "give up your child support" there would not be 1000's of people in prison tonight for failure to pay their child suport.

The father asked me to sign my rights over to him about a year ago. It was a one night stand and he begged me not to abbort that he would raise her. Now that I signed my rights away liked he asked me to a year ago, now he's filing for child support now.