First, a Living Will is a heath care declaration regarding the care a person desires should they be hospitalized. They essentially appoint aproxy to make those decisions. I assume, that instead, you mean a testamentary will.

If a person dies without a will, they are said to die intestate. If they do, the states intestacy laws determine how assets are apportioned.

In Kansas the intestacy statutes can be located at http://law.justia.com/kansas/codes/chapter59/article_5.html

The critical portion is listed below.

PLEASE CLICK ACCEPT

59-506. Surviving children or issue. If the decedent leaves a child, or children, or issue of a previously deceased child or children, and no spouse, all his or her property shall pass to the surviving child, or in equal shares to the surviving children and the living issue, if any, of a previously deceased child, but such issue shall collectively take only the share their parent would have taken had such parent been living. If the decedent leaves such child, children, or issue, and a spouse, one-half of such property shall pass to such child, children, and issue as aforesaid.

After rereading that --in California - intestacy succession is found here