What degree of burns requires a skin graft?

Third: A third degree burn or damage to the deeper dermis may require a skin graft to close the wound. This would be determined by a plastic surgeon

Depends: The answer to your question depends on the size of the burn and the depth of the burn. A 3rd degree burn is a full thickness burn involving all layers of the skin. If it can't be excised and closed primarily, it will likely need a skin graft. Some partial thickness burns (2nd degree) may require grafting also if they cannot heal in a reasonable amount of time.