Who is responsible for Aunt's funeral?

No one is responsible unless she left a insurance policy or a will with an appointment. She would then have to have assets to pay for arrangements. It is not illegal for you to get involved. The funeral home will not care who pays. If he died with no estate then you could be stuck for the money if you pay. If she left an estate you can sue to recover, or submit a bill to probate. You need to fine out about these things