There is little basis under the law for simply discarding your children. One way or the other, he still has to pay child support. No one can force him to participate in their lives. What is to be gained? If the ex remarries down the road, there may be an adoption. He can agree to that.
We do not have a client/attorney relationship until you make an appointment, we discuss your case face to face, I accept a retainer, and we explictly agree to enter into representation.
He cannot simply "give up" his rights without there being someone to receive them through adoption.
Please note that my answering this question, does not in any way mean I represent you for this, or any other case. You need to seek that actual face-to-face advise of any attorney in your area who can advise you further as to your rights.