Dying without a valid will is called dying “intestate.” If you die without a will, the laws of your state will govern how your assets are distributed. Whether you are single or married, it will be the laws of your state that determine how your property is transferred. You may also pay more in taxes for large estates.
To find an example of Kentucky's property-distribution laws, go to http://www.ca.uky.edu/agc/pubs/fcs5/fcs5425/fcs5425.pdf and access the article "Estate Planning: Wills and Probate in Kentucky." See page 2 for diagrams of “Property distribution for a person with a surviving spouse who dies without a will in Kentucky” and “Property distribution for a person with no spouse who dies without a will in Kentucky.” To review your own state laws regarding property distribution, check with your state bar association.