“I have a 17 yr old daughter that wants my boyfriend to adopt her. Her father said he would sign a paper to give up his rights. My boyfriend would like to adopt her. Can this be done in the state of NC without me giving up my rights?”
That will depend entirely on the laws in the state of North Carolina, and you should consult an adoption attorney in North Carolina. It would, however, probably be easier to do if you and your boyfriend got married first, and if you do it before she turns 18.