Since the focus of my website is the county courthouse, I'm going to share with you how the 254 counties "support the court system" in Texas.
The website Texas Courts Online is an excellent site for general and detailed information about the Texas state court system.
Use this LINK to access a pdf of the document Court Structure of Texas for a flow chart overview of the court system.
Another useful document is The Texas Judicial System, found in pdf format at this LINK. The following information comes from that document:
As provided in the Texas Constitution, each of the 254 counties of the State has a single county court presided over by a county judge. In addition to performing judicial functions, the county judge serves as the administrative head of the county government. In the more populated counties, the administrative duties occupy most of the time of the county judge, and the Legislature has created county courts at law and statutory probate courts to relieve the county
judge of most, and in some cases all, of the judicial duties usually performed by that office.
Because the Constitution limits each county to a single countycourt, the Legislature has created statutory county courts at law in the larger counties to aid the single county court in its judicial functions.
The district courts are the trial courts of general jurisdiction of Texas. The geographical area served by each court is established by the Legislature, but each county must be served by at least one district court.
In sparsely populated areas of the State, several counties may be served by a single district court, while an urban county may be served by many district courts. District courts have original jurisdiction in all felony criminal cases, divorce cases, cases involving title to land, election contest cases, civil matters in which the amount in controversy (the amount of money or damages involved) is $200 or more, and any matters in which jurisdiction is not placed in another trial court. While most district courts try both criminal and civil cases, in the more densely populated counties the courts may specialize in civil, criminal, juvenile, or family law matters.
As of January 1, 2012, Texas had 456 District Courts. Of those 456 Districts, 359 served a single county and 97 Districts covered more than one county.
For example, Loving County (population 82) is part of the 143rd District Court, based in Monahans, seat of Ward County. The 143rd District Court covers 3 counties: Loving, Reeves and Ward.
At the other end of the scale, Harris County (population 4,092,459) is home to 59 District Courts, each of which serve only Harris County.
The bottom line is this: each of the 254 Texas counties has a single Constitutional County Court. In the smallest (population) counties, that's it. So those little courthouses in counties like Loving don't have a District Courtroom, but they do have a Constitutional County Courtroom. And, large (population) counties like Harris have to construct multiple buildings to house all of their District and Statutory County Courts.
As the population of Texas grows (it's over 25 million and counting) expect to see even more District Courts created and therefore, more county court buildings designed and constructed to contain the new courtrooms and offices. See Fort Bend County for a good example.