If your children have always lived with you, and your ex got custody of one and not the other...why is that? What were the grounds? Second, you have an obligation to those children whether it is financial/emotional or just financially. Like people have said over and over again, it is highly unlikely that you can "give up your rights" and not pay child support if there is no one there to adopt them. Can I ask "why" you would "give up" and forfeit the most special gifts that you could ever receive in your lifetime? (your children) Besides, just like fathers that don't want to pay child support, you play you pay. You are responsible for those children. With the laws the way they are now, you have to pay child support regardless if you want to be a part of their lives. I would highly consider counseling for you, sounds like your ex has indeed "gotten the best of you". But like I said in the beginning, how what were the reasons that one child was taken, how come not both? What could he have on you that you would give up on your children?