Caregiver grandson live in told by grandmom home is his when she passes. She passed. Now what does he do? Nothing in writing, no POA.

I am not a lawyer, laws vary by state, ...

If I understand correctly, nomination papers are beneficiary designations.

In general, real estate transfers must be in writing. I believe the claim order would be:
1) transfer on death beneficiary
2) heirs as specified in will
3) interstate succession law of given state: mine is: spouse, child, parent, siblings, ...

So, uncle gets bank account but may chose to share or pay final expenses to honor Grandmoms wishes.

Where it gets more complicated is with the deceased child ( Mom). If Mom outlived Grandmom, then her husband may inherit based on her will or interstate succession. If Mom passed before Grandmom, then Grandmom's arrangements apply.

However, there are different approaches to splitting among Grandmom's children. If the approach called per stirpes applies then Grandson has a claim to Mom's share, shared with mom's other children, if any.

Consult a lawyer. Anyone can sue for anything. Is there any evidence like a caregiver contract or receipts for out of pocket expenses, a video of the family all agreeing to the grandson getting something, ...?

No Will then someone needs to go to Probate and become an Administrator. That person will be given a short certificate to handle grandmoms finances and find out what her estate encompasses. If there is a house, then its either sold or one of the siblings will need to buy the others out. Never heard of a nomination paper. The State will step in since there is no Will. The husband may be entitled to a % of her estate and then the children. In my State the spouse gets 75% and the children 25% split between the children. I suggest a lawyer. His fees will come out of the estate.

Since your mom has kids, they will most likely get her 25% of the estate and her husband gets nothing. If there were no kids, then depending on the state, your moms husband might be entitled to her share. But that’s moot since she has kids. Her kids are first in line.

What do you mean by 'nomination paper'?

If there is no will, your state's intestacy laws will apply. I think your stepfather will probably be out in the cold, but if he argues the dispute could easily swallow up a small estate so if you're on speaking terms with him, discourage him. I don't at all have any confidence in this either, but I'd have thought that you as her child might have a better claim on her theoretical share of her mother's estate than he does.

What's this about the house? Are you the caregiver grandson, living in your late grandmother's house and hoping to stay there? Unless your uncle/aunt(s) agree I'm afraid you won't have a leg to stand on.

Does it leave you in difficulties? When did you move in to your grandmother's house?