Step-parent Adoption. Many people often ask us if their child’s non-existent parent can relinquish his or her parental rights or whether the court can terminate his or her parental rights. This can typically only be done concurrently with a step-parent adoption. If the absent parent is willing to relinquish his or her parental rights, this process is usually rather smooth and quick. It is highly recommended that you consult with the absent parent to determine his or her willingness before moving forward. Oftentimes, they are eager to relinquish their parental rights knowing that the child will be better off being adopted.