“I am an 18 year old who has had an affair with a 33 year old married man. I have gotten pregnant, and I am about 2 months along. The biological father and I have terminated our relationship, and I want nothing to do with him. I don’t want his money, and I don’t want him to have any parental rights to my child. He has agreed to terminate all of his parental rights. He wants nothing to do with the child. How do I establish this termination of parental rights legally? Thank you so much for your help!”
You can’t. Unless there is somebody else lined up prepared to adopt the child as its legal father.
And guess what? It’s not just your child. Like it or not, it’s his child too. And always will be, even if he has nothing to do with it (which will screw the child up for life, by the way).
In addition, even if you choose to leave the father alone, and have nothing to do with him, if you ever request child support through the state, and if you ever accept any state aid, the state will force you to reveal who the father is, and they will go after him. So one way or another his wife is likely to find out.