If a stepparent wants to adopt his or her spouse’s children from another marriage, the other parent will need to give up his or her parental rights. This termination of parental rights is a legal process that leaves your ex-spouse without rights. Your ex-spouse can give up these rights voluntarily, or, in certain circumstances, you may be able to receive a court ruling that orders the termination of parental rights. During this process, you will maintain your parental rights.