In Utah: First, you must understand that you cannot merely "sign away your rights," to a child. If what you mean is that you desire to have your parental rights terminated, the only way to do that is through filing an action in the court to have an order of the court issued that terminates your parental rights. But if and when your parental rights regarding a child are terminated, you are correct in understanding that you also have no further obligation to support that child.
Answered on Dec 23rd, 2013 at 11:31 PM