Can a father give up parental rights in the state of Alabama?

Can it happen if the mother has a new partner who wants to adopt.

Also has happened on rare occasion without adoption with agreement between mother and father, but this does not stop the child support. So the father still has the obligation to pay. So there is little reason to do it, or spend the legal costs to try, since you don't get anything, if you don't want to use your rights, just don't