When a child shall have been relinquished by written instrument, as provided by sections 43-104 and 43-106, to the Department of Health and Human Services or to a licensed child placement agency and the agency has, in writing, accepted full responsibility for the child, the person so relinquishing shall be relieved of all parental duties toward and all responsibilities for such child and have no rights over such child. Nothing contained in this section shall impair the right of such child to inherit.