Legal Question in Family Law in Georgia

Unless someone else is adopting the child, there is no such thing.

When you say sign over your parental rights, do you mean give your husband full custody without visitation? If so, that can be taken care during the divorce proceeding. However, that won't relieve you from paying child support.

Under OCGA 15-11-94, there are grounds for termination of parental rights. However, this has to be done after a petition has been filed and the court determines it is in the best interest of the child.

Moreover, because the children are in a different state, that state's laws may apply regarding these matters. Therefore, I recommend you contact counsel in that state or repost this same question as if you lived in that other state.