How can a father give up his rights with out paying child support?

A friend of mine wants to give up his rights not because it has anything to do with the children, but because his ex wife is very intrusive he wants to give up his rights and move on in life with out being threatend or stalked anymore.. I understand that yes, he had two children and it is his responsibility but there is no reason why he should have to be his ex wifes “dog”, and have to listen or do anything she says because she thinks the world revolves around her. He’s also in a relationship and the couple is doing great together.. their only problem that has caused any kind of turmoil is the mother.. She’s trying everything to ruin his life when he has done nothing but taken care of her and his two children.. And the sad thing about this whole situation is that this guy is such a sweety and these kids may not even be his because she has cheated on him numerous times and broke his heart.. but he is too afraid to know the actual truth so he will not do a test. The mother, blows up his phone with calls, and texts, and even stalks him to the point where he can not get any peace. She threatens him with calling the cops, making him pay child support again, and court so he will abide by her rules.. There have been times where the mother was so desperate to get rid of her children that she actually dropped them off in the middle of the street and drove off like a bat out of hell.. She tries her best to push them on him when she wants to go out to clubs and look for a new hubby when even though the father is busy, she just can’t go out and drop them off at the sitter..

So I’ve talked to him and he plans on moving. He thinks it is best for him and his girlfriend. They are so good together but he can not live his life in peace with out his ex being a psycho. She even has her friends send nasty messages on a social site to his innocent girlfriend who wants nothing to do with her or the situation.. He feels for his children, but they’re fine with out him, they honestly don’t even really care to see him because they are happy where they are, but mom tries and pushes them on dad.. So my question is, what can he do? Can he give his rights up, and can he do it with out having to pay child support?