The laws of each state may effect who is appointed with Power of Attorney.
Generally, spouses make decisions for an incapacitated adult.
If one is not married, state law may permit the children of that person to make medical decisions, assuming that all of the children agree on the care to be provided.
But when such health care decisions cannot be agreed up, in most situations the children of the adult who is incapacitated may need to petition the probate court or other court of competent jurisdiction to obtain an order authorizing them to make medical and health care decisions for the incapacitated adult. Such a petition may require the services of a local attorney; you can find a lawyer for FREE at Standard Legal’s Attorney Find page.
This type of situation underscores the need to obtain a properly drafted and executed Living Will and Power of Attorney for Healthcare in advance of such issues. Standard Legal Network offers both legal forms software products on its web site: Living Will | Power of Attorney.