If my father dies without a Will and I am his only child, what will happen with his estate?

The last part of your question has a great bearing on the advice here.  In Texas it is called an "informal marriage," rather than a common-law marriage. Under § 2.401 of the Texas Family Code, an informal marriage is established in one of two ways: either by declaration (registering at the county courthouse without having a ceremony), or by meeting a three-prong test showing evidence of (1) an agreement to be married; (2) cohabitation in Texas; and (3) representation to others that the parties are married. Now, in 1995 an update to the law added an evidentiary presumption that there was no marriage if no suit for proof of marriage is filed within two years of the date the parties separated and ceased living together. So if his common law wife did not bring such a suit she would not be considered his "wife" for inheritance purposes, or at least that would be your stance in probate.  When some one dies with out a Will they are said to have died "intestate" and that would mean the intestacy statute in Texas would govern distribution.  Anything jointly held passes to the joint owner upon death.  Any that has a designation of beneficiary that was properly filled out - and not subject to challenge on another basis - passes to the beneficiary.  Like life insurance policies. You should consider a guardianship and conservatorship for your Dad.  Please seek legal help.  Good luck.