Who is responsible for funeral costs when no Will exists?

The estate for the deceased is responsible for funeral costs. Based on your facts, the children are all entitled to equally inherit from the deceased parent's estate. Before the children can inherit though, there may need to be a probate as you do not indicate what the deceased owned and owed. I suggest that the 4 children get together and decide which of them is in the best position to administer the estate. By administering the estate, I mean figuring out what is owed and owned, paying the estate bills from estate assets and overseeing the orderly transfer of assets from the deceased to the children. Ideally, it should be a child who lives in the same state as the deceased or closest to the deceased or in the county where the estate will be probated. It should also be someone who is detail-oriented, good with paperwork and who is fiscally responsible. If the estate is overly complicated or large, then the personal representative should consider hiring a probate attorney to help him or her probate the estate. If nothing else, the chosen representative should consult with a probate attorney to get a better feel what is required. The estate will be probated in the county where the deceased lived at the time of death. Funeral expenses are paid out of the estate. If a family member pays for the funeral then that person should submit a claim to the estate to get reimbursed. If there are insufficient estate assets, claims are paid in order of priority as set forth in the statutes. Funeral expenses are not given priority for full payment. Why do you need a definition of next of kin? If there is no will and no spouse then all adult children inherit equally. If an adult child died before the parent, then the dead child's children, if any, would take their dead parent's share. If the children are already squabbling, that does not bode well. In such case, any of the children can contact a probate lawyer and file a probate petition. The others can object and if a written objection is filed then the court will decide which of the 4 children should be the personal representative.