I've moved this to Family Law, not sure what it has to do with Taxes.

If you are not on the birth certificate, then you have no rights to sign over. If the other man is on the birth certificate, then he is the legal father until a court rules otherwise. So there is no need for him to adopt or for you to sign anything.

So the first thing is you need to define what you want to do. If you don't want to have anything to do with this child, then you do nothing. If you want to be a father, then you need to go to court to have yourself declared the legal father and to enforce your rights.

I've merged your two threads.