Estate Law Questions? Ask an Estate Lawyer.
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If individual(s) die without having a will or a trust, they are deemed to have died "intestate" and the state's intestate succession laws will determine how the interests in the estate are determined. Each of your parent's estates will need to be distributed through probate (as will each of your deceased sibling's estates) in order of their death.
This can get a little bit complicated, and I would recommend retaining a lawyer to help (you will need a probate attorney (this is a trusts and estates attorney that works with the courts)).
The Texas intestate succession statute is explained here: http://www.nolo.com/legal-encyclopedia/intestate-succession-texas.html