I am often asked if one parent can sign over his or her rights to a child. Usually, this question comes when either the noncustodial parent has had little involvement with the child, or would like less responsibility regarding the child; or, when the custodial parent wants to eliminate the noncustodial parent’s involvement with the child. The short answer is no; you cannot sign over your rights. In the courts eyes, if you made a kid, you are responsible for that kid. You don't get to quit being a parent just because you are tired of paying child support, or tired of dealing with a difficult teenager or uncooperative co-parent.
And while we are on the topic: Never, ever, tell your child that you plan to voluntarily terminate your rights to them. It does not matter if your relationship has deteriorated, it does not matter if you don’t mean it, it does not matter if you said it in the heat of the moment, it does not matter if you regret it later; don’t tell your kids you will sign them away. You can’t actually do it, and saying so will surely destroy your relationship with them. If you think child support is expensive, try paying for therapeutic family counseling.
Likewise, if the non-custodial parent has been extremely distant, or has become difficult to work with, custodial parents cannot have the non-custodial parent’s rights taken away. It does not matter if the non-custodial parent is unreliable, or an inconvenience to you; until a court says otherwise, that parent is entitled to a relationship with the child and vice versa. Now, does that mean you are without any legal remedy? No, you can seek a modification of your current decree (or an initial action, if you don’t have a decree yet). If the court finds there is a good reason, it can take away the non-custodial parent’s decision-making authority regarding the child, and extremely limit or, in rare occasions, stop the non-custodial parent’s visitation. Such a restrictive custody order can feel like a parent’s rights have been severed; however, unless the child becomes adopted or is taken into state custody, the parent will always retain some level of legal rights to the child.