The power of attorney won't be effective because it terminates at death. If there isn't any Will, the rules of intestate succession determine inheritance.  Intestate means dying without a Will.  Under intestate succession, the surviving spouse inherits the entire estate.  If there isn't any surviving spouse, the estate will be divided equally among the surviving children.  If there is a deceased child who had children, the grandchildren will inherit the share their deceased parent would have inherited.