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I'm sorry to hear about your situation. Yes, you can give full custody to your son's father, but that doesn't terminate your rights. You could also file for a voluntary renunciation of rights, but most of the time even that does not terminate your obligations.
Giving up your rights will not terminate your child support obligation. Parental rights include both rights AND responsibilities. You can freely give up those rights, but need a judge to sign off on relieving you of your responsibilities (child support). And this is almost exclusively in the context of an adoption.That is, when someone else is willing to step in and be declared the legal parent of the child and support the child, a judge will then relieve the biological parent of that obligation. giving up parental rights (voluntarily) rarely does much for you, as the parent. Think of parentage as a basket of rights and responsibilities. Some are things that you can do (rights) and some are things that you have to do (responsibilities). When you voluntarily give up your parental rights, you give up only the rights in this "basket", but retain the responsibilities. Even if the judge signs off on the termination of rights, the obligations remain unless the judge signs off on the termination of those as well.
Now you can enter into an agreement with the father that you won't pursue custody / etc... if he doesn't seek child support from you. And if this other woman wants to adopt your son, the judge would likely sign off on the termination of your rights AND responsibilities (child support). But in the absence of a court order saying that you don't have any more child support responsibility, it's still possible that he could come after you for child support.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!