Dying Intestate Kansas

Married with no children
If the decedent leaves a spouse and no children nor issue of a previously deceased child, all the decedent’s property shall pass to the surviving spouse.
Married with child or children
If the decedent leaves a spouse and a child, or children, or issue of a previously deceased child or children, one-half of such property shall pass to the surviving spouse and the other half will go to that child or children or their issue.
Order of estate distribution if spouse survives
1) children
2) surviving spouse
No spouse survives but there are other relatives
The estate passes to those relatives in the order shown below.
Order of estate distribution if no spouse survives or decedent was not married
1) surviving parents
2) deceased’s siblings and their descendants
3) all other relatives in order of descent by degree of blood.  That means, the closest relatives receive the estate distribution first.
No surviving relatives
The estate will go to the state of Kansas.
State link
http://kslegislature.org/li_2012/b2011_12/statute/059_000_0000_chapter/059_005_0000_article/
Special notes
The people entitled to inherit are limited to those not separated from the deceased by more than the sixth degree.