If something happened to you (death, incarceration of interdiction) they would have a right to visitation. You need to get a custody judgment between you and the father. Then you could do a custody by mandate from you to them.
Every situation is different and you should consult your own attorney to go over all the particular facts in your case. The answer given is only intended to provide general guidance regarding rights and responsibilities.
If your parents are the only ones able to provide a stable home for the child and have done so for while one or both could be awarded custody. You and your parents should sit down with a family law specialist to discuss your options and strategy.
This response does not creat an attorney client relationship. In all cases, I recommend you seek a paid consultation with an attorney with expertise in this area.
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