Estate Law Questions? Ask an Estate Lawyer.
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If you are asking about laying a claim to it against all others, then that is what is called "adverse possession". Under TX law, if you can maintain exclusive and sole possession of the property without permission from the owner for 10 years, you can legally claim it as your own by filing a "quiet title" action in court against the legal owner (i.e. his estate)
So in order to prevent it from being sold for back taxes, it would probably be a good idea to pay them and then take physical possession of the land by going onto it and making improvements like cutting weeds and brush and maintaining it until that 10 years passes.
If you went to file a probate case to settle his estate, then all his legal heirs would become the owners and you would have to buy out their interests in order to become the owner.