At first it would seem you may own this property, however these are the situations that adverse possession was created to remedy and may very well apply to this case. Basically if you think you own the property and possess it continuously and exclusively for a period of 10 years then you may have the ability to have a court grant you title to the property even when you were mistaken as to your ownership.
The law of adverse possession in Texas was articulated well in the following case.... http://www.supreme.courts.state.tx.us/opinions/HTMLopinion.asp?OpinionID=2000871
Here is a relevant excerpt:
Under Texas law, adverse possession requires "an actual and visible appropriation of real property, commenced and continued under a claim of right that is inconsistent with and is hostile to the claim of another person." Tex. Civ. Prac. & Rem. Code § 16.021(1). The statute requires visible appropriation; mistaken beliefs about ownership do not transfer title until someone acts on them. See, e.g., Bywaters v. Gannon, 686 S.W.2d 593, 595 (Tex. 1985). Thus, there must be adverse possession, not just adverse beliefs.
The statute requires that such possession be "inconsistent with" and "hostile to" the claims of all others. Joint use is not enough, because "possession must be of such character as to indicate unmistakably an assertion of a claim of exclusive ownership in the occupant." Rhodes v. Cahill, 802 S.W.2d 643, 645 (Tex. 1990) (quoting Rick v. Grubbs, 214 S.W.2d 925, 927 (Tex. 1948)) (emphasis in original); McDonnold v. Weinacht, 465 S.W.2d 136, 141 (Tex. 1971). Here, Haliburton shared use of the strip with the Buddes, so her use was not inconsistent with or hostile to their ownership. See, e.g., Brooks v. Jones, 578 S.W.2d 669, 673 (Tex. 1979) ("It has long been the law in Texas that when a landowner and the claimant of an easement both use the same way, the use by the claimant is not exclusive of the owner's use and therefore will not be considered adverse.").
If the people who have occupied the property for 50 years under the belief they owned it were to file a quiet title action, they may find success and the court order that they know own the property. This may or may not have an impact on the mineral rights and you may find it to your advantage to simply execute these quit claim deeds to protect your own interests.
I strongly advise you to seek local counsel and let them review this situation (and the property itself... take pictures). If they determine you would lose an adverse possession action, you will likely want to sign these deeds.
Please reply if I can help further.
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Edited by JD on 2/5/2010 at 3:10 AM EST