Since he is the father of the child, he could get visitation rights if he brings the action to court. But there is a great chance that you will be granted full custody if the court finds that it is for the child’s best interest to stay with his mother. Just to make it clear, even if you have full custody, he may still get visitation rights if the court grants it. Talk to a family law attorney to find out how you can handle the situation with your ex boyfriend while keeping the child’s welfare a priority.