At least in the States it depends on individual state laws. Here in SC
for instance the law's set as follows if a person dies intestate with no spouse.
1) To the issue of the decedent
2) If there is no surviving issue, to his/her parents
3) If there is no surviving issue or parent to the issue of the parents
4) Grandparents or issue of grandparents
5) Great-grandparents or issue of great-grandparents
6) Stepchildren or issue of stepchildren
7) State assumes estate
As you can say, it's HIGHLY unlikely that there won't be at least one survivor in there somewhere to inherit. But if everyone eligible to inherit from you were to pre-decease you, then South Carolina gets your estate.
South Carolina - too small to be its own country, too big to be a mental asylum.