I live in Georgia and I'd like to adopt my 5 year old step daughter. My wife has sole legal and physical custody of her. The biological father was exempt from paying child support and all/any visitation is up to her discretion. This was agreed upon in their uncontested divorce. So did he relinquish his rights by agreeing to these terms in the divorce? If not, was agreeing to those terms enough to involuntarily relinquish him of his rights if he did not want to do so (out of spite!)? He makes little to no effort to have a relationship with the child. He was physically and verbally abusive to my wife during their marriage (we have the police reports/pictures). He also has a felony on his record. While I THINK we are ready to prove that adoption is in the best interest of the child (she wants to know why her last name is different than the rest of the family), I couldn't help but ask for advice/opinions when I came across this website.

So did he relinquish his rights by agreeing to these terms in the divorce?
No, because he has never voluntarily and in writing surrendered all of his rights to the child .

If not, was agreeing to those terms enough to involuntarily relinquish him of his rights if he did not want to do so (out of spite!)?
In my point of view it is a very questionable advantage./but it is only my view!/. Firstly-your wife VOLUNTARY agreed to the conditions " No child support and visitation on my discretion"... Then you cannot use Termination of parental rights laws where it is stated:
O.C.G.A. 15-11-94 Grounds for termination;
(3) The parent has abandoned the child or the child was left under circumstances that the identity of the parent is unknown
(C)(ii) To provide for the care and support of the child as required by law or judicial decree;
Secondly-your wife has never filed for child support that it is her fault,too.
/In Pa the Supreme Court stated that non-paying child support when the mother had never asked for is not a ground for TPR.Only failure to pay ordered support is a ground for TPR/

He makes little to no effort to have a relationship with the child...and all/any visitation is up to her discretion. This was agreed upon in their uncontested divorce.
That may / or may not / put you in trouble. The trouble is that visitation must be"up to her discretion".

5-11-94. Grounds for termination; other dispositions


(a) In considering the termination of parental rights, the court shall first determine whether there is present clear and convincing evidence of parental misconduct or inability as provided in subsection (b) of this Code section. If there is clear and convincing evidence of such parental misconduct or inability, the court shall then consider whether termination of parental rights is in the best interest of the child

To my knowledge Georgia has different laws concerning child abandonment and neglect than the other states.. Thus you do not have to accept my post as the whole truth.
I guess Fr Chuck will be more helpful / He lives in Ga/;)

The biological father was exempt from paying child support and all/any visitation is up to her discretion.

I guess whether it may invoke estoppel or not.
/Estoppel - a bar or impediment (obstruction) which precludes a person from asserting a fact or a right, or prevents one from denying a fact. Such a hindrance is due to a person's actions, conduct, statements, admissions, failure to act, or judgment against the person in an identical legal case. /

No, he gave up no "rights" at all, he merely gave up time with the child and the mother for some reason gave up child support.

Not sure why the father was exempt, normally there is no such thing, in Georgia even unemployed will have a small amount to pay.

But the father still has the right to go back to court and ask for modifications of the current court orders. So he has all of his rights, he just merely has a very poor agreement from his side.

To adopt, you will need the father to sign over his rights. Which he has little need to do, since he is not having to pay child support right now.

As for as taking his rights away, if he does not even show up to fight. Next merely changing a name is not enough to be best interest, is there a danger or need that is not discussed yet

... He makes little to no effort to have a relationship with the child. He was physically and verbally abusive to my wife during their marriage (we have the police reports/pictures). He also has a felony on his record.

... I THINK we are ready to prove that adoption is in the best interest of the child (she wants to know why her last name is different than the rest of the family) ...

I don't think all of those combined meet a best interest test. And, as GV70 has stated, "clear and convincing evidence of parental misconduct or inability" must be proven before a best interest test is even looked at. I don't see that you can show such parental misconduct or inability.

You are probably going to need his consent.