If a mother dies without a Will, are the surviving adult children entitled to anything or does everything go to the stepfather?

When a person dies without a Will, the rules of intestate succession determine inheritance.  Intestate means dying without a Will.

In the situation you described, the surviving spouse would inherit the entire estate.  If there isn't any surviving spouse, the estate will be divided equally among the surviving children.  If an adult child died and had surviving children, those surviving children would receive the adult child's share of the estate.