If you are otherwise fit as a custodial parent to assume sole/primary/legal custody and the father is consenting (he can't totally "give up his rights" unless there's a custodian willing to adopt), there is little chance that the grandparents will share custody with you.
This would only occur in the instance where you were found to be abusive or neglectful, and then the grandparents might gain primary custody or become guardians. You don't have much to worry about here, but having an attorney to deal with the grandparents or their attorney would reduce your stress levels.
Grandparents don't ordinarily have a right to custody or even to participate in a custody matter or file petitions where the biological parents are in the picture and are otherwise fit to be parents.
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The court will not order joint custody to you and the child's grandparents. Either you'll get custody or they will get custody.
The above answer is intended for informational purposes and is not legal advice. It does not constitute the creation of an attorney-client relationship.
Unless you agree, the chances are nil.
I am an attorney with over a decade of experience in Matrimonial and Family Law with offices in Brooklyn and Manhattan. I have experience in all five boroughs as well is Nassau and Suffolk County. The opinion expressed in this ad based upon the limited information provided and do not indicate an attorney-client relationship