I have been with my boyfriend for the past year and a half. Before we got together he messed with this girl only a few times, after she found out we were together she told him she was pregnant and made our lives a living hell. He never had a relationship with her and told her that he wanted nothing to do with her or that baby. What does he need to do in order to sign over ALL his PARENTAL RIGHTS? Does she have to agree to it as well or what? We need to know so that he can do it.

I think she has to agree or the judge won't grant it unless he is a sex offender, drug dealer, or something like that. He will have to pay support if she goes for it, however, he is not obligated to take visitation. I would get a DNA test to be sure.

As others on this thread have said time and time again, there really is no "signing away of one's parental rights" unless it's to clear the way for someone else to adopt the child. Has he ever been proven to be the father of this child? If not then it's a moot point. If he has, then she can pursue him for child support and he can pursue her for visitation. But not having visitation doesn't keep him from having to pay child support.

Has she had the baby already?
It might be a good idea to make sure she's actually pregnant. Some women like to say that they're pregnant just because they're angry at there x boyfriend.
If she is pregnant or has already had the baby, get a paternity test. This can be done before or after the baby is born.
If it is his, he'll probably need her consent to give up his parental rights, as far as child support goes, it will depend on the judge and his income.
What do you mean by they never had a relationship? They never dated, or they never had sex? It's hard to have a kid without sex.
Really it sounds like the girl is trying to get back at you. If you've been togeather for a year and a half then and your boyfriend has been with you the whole time, it's not his. If she appears a little pregnant, either your boyfriend is cheating on you or the girl is telling him that because she dosen't like who the father really is. Just look in to that scenario a little.

Good Luck