Generally, no. A parent cannot simply "give up their rights" to a child. There are several reasons for this, but most importantly a child should be entitled to the benefits of having two parents. The most common way to give up rights, without a fight, is to have your new spouse adopt the child and terminate the rights of the biological parent simultaneously. Again the reason is that this would ensure that the child has two parents. If you are serious you need to speak to an adoption attorney about your rights and responsibilites.
Bradley L. Henry, J.D.
800 S. Gay Street
Knoxville, TN 37929
(865) 521-7433 (Fax)
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