Looks like BLM manages a whopping 11,000 acres near Amarillo. For comparison, BLM manages about 23 million acres in Utah (42% of the state).
OK, here's the skinny on public land in TX, otherwise known as a brief history of land title in our illustrious state.
In most Western states, the legal title to most (if not all) land was originally held by the federal government of the United States after being obtained (or stolen, but I digress...) from Native American tribes. In Eastern, Midwestern, and Southern states, title to land that was not privately held was transferred to the United States when the land was obtained from a foreign power or from Great Britain.
Texas is different from most states. The title to all land in TX was originally held by Spain and transferred to Mexico after it gained its independence. The Mexican government was severely strapped for cash and sold huge swaths of TX land to private owners to raise funds, a process that was greatly accelerated by rampant speculation; this practice continued after the Republic of Texas was established, as the new government had many of the same problems that the Mexicans did, i.e. a huge territory to protect, very little population, and a lack of readily exploitable natural resources in the better-populated and more-accessible coastal areas.
Here's the key to all of this: when the Republic of Texas finally agreed to join the USA, the remaining public Republic of Texas land went to the
state government rather than the US federal government. Although statehood fixed some of TX's problems, the new state still had a very limited tax base; agriculture was not firmly established, commerce was constrained by a lack of reliable transportation, and the booming petrochemical industry didn't exist yet. Hence, the state resumed selling land, and sold almost all of it by the close of the 19th century. All that remains today are some small, odd-shaped, and/or inaccessible tracts, along with tracts "discovered" (so to speak) when someone resolves a long-ago surveying mistake.
Result? Almost all of the land in TX was already privately held before the modern federal BLM and national park systems were even established.