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Dear JAGUEST-27084537 - As the father of your child he will have parental rights however those may be limited by the court based on his past record. There is no question that you will have custody and if he wants visitation he can apply through the courts and you would have the right to object or to at least request only supervised visitation.
He will also be responsible for child support until your child becomes and adult. Until he files for his parental rights he will have no power to do anything. Even if you don't put his name on the BC he could still apply for parental rights so it really doesn't matter unless you want to seek child support now.