Is It Legal?
What happens to the federal courts located in Texas?
The federal courthouses sit on Texas soil, staffed largely by Texans, and an independent Texas already has a complete, fully functioning court system of its own. The federal courts in Texas would be wound down or converted in the transition, and the Texas judiciary would carry the full load, the way it already carries the overwhelming majority of it.
Texas already runs a complete court system
This is the fact that defuses the whole question. Texas has its own judiciary from top to bottom: municipal and justice courts, county courts, district courts, fourteen courts of appeals, and two high courts, the Supreme Court of Texas for civil matters and the Court of Criminal Appeals for criminal matters. These courts already handle the vast majority of all cases in Texas. The federal courts here handle a defined slice, federal crimes, federal civil questions, disputes between citizens of different states, and the like. Independence does not create a courthouse vacuum, because the Texas court system is already there, already staffed, and already doing most of the work.
What the federal courts here actually are
The federal judiciary in Texas consists of four U.S. district courts, the Northern, Southern, Eastern, and Western Districts, plus the federal appeals layer above them. Their authority comes from the U.S. Constitution and acts of the U.S. Congress. When Texas is no longer part of the union, that authority no longer extends to Texas. The buildings, the records, the staff, and the pending matters do not disappear. They are addressed in the transition.
The transition handles the buildings, the records, and the people
A negotiated separation deals with federal facilities and personnel as a matter of course. The most likely outcomes for the courthouses are the same menu Texas applies to any federal property on its soil: transfer to Texas, often for conversion to Texas judicial use, or another arrangement settled between the two governments. Court records get transferred or copied so nothing is lost. And the people matter most of all. Federal judges, clerks, and court staff in Texas are overwhelmingly Texans who live here, and they represent exactly the kind of experienced legal workforce an independent Texas wants to keep. Many would simply continue their careers inside the Texas system.
Jurisdiction moves to Texas courts, cleanly
Going forward, every case that a federal court in Texas used to hear has a natural home in the Texas system. Crimes become offenses under Texas law, tried in Texas criminal courts. Civil disputes are heard in Texas civil courts under Texas law. Texas already has courts of general jurisdiction that can hear essentially any kind of case, which is precisely the capacity a national court system needs. There is no category of dispute that an independent Texas would be unequipped to adjudicate.
The federal cases already in the pipeline are handled in the transition
Cases pending in federal court at the moment of independence are exactly the kind of practical matter the separation agreement resolves: which forum finishes them, how appeals are routed, how records move. This is ordinary transition work, and it is covered in its own question below. The headline is simple: nothing is dropped. Pending matters are wound down or transferred under agreed rules.
The bottom line
The federal courts in Texas lose their authority at independence, and their buildings, records, and people are handled in the transition, often by folding them into the Texas system. Texas already operates a full court system that handles most cases today and is fully capable of handling the rest. Texans would be judged in Texas courts, under Texas law.