I am sorry for your loss. In Texas, there are several choices with respect to what type of probate is best in any particular matter. Choosing the correct option depends upon the assets (and debts) involved and if the heirs are in agreement on certain matters. If a Decedent dies without a Will, there is no way to have an executor; however, without a Will, it is still possible to have an administrator appointed (either independent or dependent). It may be better to step back a moment and consider all the options. If no formal administration of the estate is necessary, there are two options: 1. Small Estate Affidavit (estates of $50,000 or less, excluding homestead, and no debts other than perhaps a mortgage); or 2. Proceeding to Determine Heirship. If an administration is necessary, there are still two options: 1. Independent Administration (if all heirs agree on the appointment of an IA); or 2. Dependent Administration (when all the heirs do not agree on the appointment of the administrator; or if the Administrator wants the Court to be involved with managing the debts and creditors; DA is the more expensive route). If either of these latter two options (IA or DA) is chosen, then along with the administration filing/proceeding, the administrator will also need to file an Application to Determine the Heirs (and the appointment of an ad litem attorney to assist the Court in determining the heirs of the estate). Often, when dealing with lots of debt and many creditors, a Dependent Administration is best since there are very strict guidelines that creditors must follow or their claims against the Estate are bared.
In Texas, if the Decedent dies unmarried with children, then the children of the Decedent (or the children’s descendants, as the case may be), share equally in both real property and personal property. I suggest that you speak with an experienced probate attorney to help you through this journey. Again, I am sorry for your loss and wish you and your siblings the best of luck.
The first responder provided you with a good summary of the options. You need an attorney to determine what is the best option for clearing title to your father's property. One issue that stands out is unpaid real estates on the two parcels since his date of death. If unpaid, there may have been a tax sale of the property.