IF the father of the baby wants to give up his rights is he still obligated to pay child support, we are not married. if the father is not on the birth-certificate and I have sole custody is he still obligated

This question has been asked and answered hundreds of times in this forum. I suggest reading through some of the previous threads for details.

The bottomline is that courts are very reluctant to terminate a parents rights, even if they agree to it. They will not do it just to allow the parent to get out of child support. In some states, the two are considered separately and rights can be terminated without removing the obligation for support. In states where termination ceases support, its even harder to get a TPR.

If the father is not on the because, that doesn't change his obligation. It just makes it harder to get support out of him. It would first require a paternity test to establish parentage.

As scott pointed out if he isn't on the birth cirtificat your first step in getting support is to go to court to establish paternaty. This means going the judge ordering a DNA test (they don't accept private ones) once the results show that it is his child then the judge will order support and visitation if he wants it. But he can't just sign over his rights with out first convincing a judge it is in the child's best interest. Also as Scott said read some of the other threads and you'll learn a lot.

IF the father of the baby wants to give up his rights is he still obligated to pay child support, we are not married.,if the father is not on the birth-certificate and I have sole custody is he still obligated
Thanks I looked at the site quickly. I have read a lot more now.