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You made your mistake by not having the father served. If you cannot locate the guy when you want to serve him papers, then you have to publish a legal notice in the paper as noted in the North Carolina Rules of Civil Procedure. Look under, "When process returned unexecuted", below. I put all the rules here for your information. Your only problem was apparently proper service, so now you have the info to proceed. Your notice is put in your local paper. Now, even when you get the publication and he is considered "served", you will still have to go to court. If he does not answer or show up, then you will get custody, and you will have to then find your son. Have your court order with you.
Rule 4. Process.
I hope this helps. I wish you the best of luck.