When there is no will, the person is considered to have died "intestate." Every state has intestacy laws that determine what happens to the property.
In Texas, the surviving spouse and children will usually inherit all probate assets. If there are no children or grandchildren, the property may pass to the spouse, parents, siblings, nieces, nephews, and/or other heirs, depending on the situation.
Intestacy laws don't apply to nonprobate property. Nonprobate assets pass directly to the named beneficiaries without court involvement.
Texas is a community property state, with different rules for community and separate property. This can introduce some complexity, especially when both types of property are present.
Texas Law