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Thanks for the question. You may have grounds for termination in this matter. you probably need to obtain a lawyer to file a petition to do so. It sounds like the mother has shown little interest in this matter to date and has not been a very good mother.
The court would require you to prove up neglect and un involvement with the child and to show that it is in the best interest of the child to terminate the parental rights. There also may be the issue of non support if she has not contributed anything.
If you feel that this is the best thing for you and the child I would urge you to proceed in this matter. Often you will find that parents like this tend to drop in and out of the child's lives, like a long lost cousin that comes by for a once every two years visit and that really messes with the kids minds and makes it even harder for people like you who are doing the day to day raising of the child. I hope this gives you some ideas in this matter and good luck to you..