He cannot do that without marrying you first, or terminating your rights as a mother.
I am exclusively a family law attorney, practicing primarily in the metro Atlanta, Georgia trial courts. However, I handle appeals from anywhere in Georgia.
Unless you are willing to surrender your own rights and make him the only legal parent, which I am assuming you don't want to do, you will have to be married and do a stepparent adoption. If you were to get married, and the biological father has no interest in being a father, you could do a stepparent adoption fairly easily with the help of an experienced adoption attorney. If marriage is not in the cards, best to leave things as they are.
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The advice of the first two answers was basically good, but not totally accurate. While stepparent adoption normally does require that the petitioner (stepfather) be married to the biological mother, the judge have the power to that requirement. If there is some good reason for that (beyond what is stated in your question I mean), the judge be willing to do that. But having said that, it's not likely. As stated, consulting an experienced adoption attorney is highly advisable.
If your boyfriend were to adopt your child, your rights would be terminated and you would cease to be the mother.
If you want to remain the mother, the only way for you to have him adopt would be for him to marry you first. Once he does that, then you need a lawyer.
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