How exactly does one go about learning which court of appeals is overarching or otherwise connected with a given county court or municipal court or JP court?

I totally get (thanks, Dr. Graves!) the concept of how much value there is in citing and quoting to a judge from previous cases from their own higher-up courts. Great... where is that kind of hierarchy published?

And are there multiple overlapping hierarchies, depending on the nature of the claim? Like if it's a criminal case, its appeal gets handled by one court, or if it's civil, then its appeal gets handled by some other court...?

every court has an hierarchy. you can google the court system for your state.

Here in New York, there are 5 courts of jurisdiction which are considered Article III courts - Supreme, Family, District, Appeals and Circuit.

Other courts (which are administrative) are municipalities and counties.

Thanks, Chris4 -

I guess I failed to mention that I have already been trying to google this quite a bit, but since this whole world of court jargon is unfamiliar to me, I've had only very limited success figuring out what terminology to search with, and even when I get the results, it's not evident to me which results are pertinent. To someone such as yourself who is seasoned in this topic, it must seem like a strange concept that anyone would be as clueless as I am... to which I can only say I'm sorry, and hope for a little help to get my head around some basics of court hierarchy... or at least the lingo so I can make sense of google results.

BTW: I'm in Texas.

You mentioned "Article III"... of what?

No apologies are necessary since we are all here to learn. Google is the closest database for searching legal cases. A few months ago, the Bar Association sued Google in an effort to remove references to court information. The Bar Association lost this battle.

For us, we have to learn the jargon because it is the language of the law and attorney.

Article III Judicial Branch
Section 1
The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish. The Judges, both of the supreme and inferior Courts, shall hold their Offices during good Behaviour, and shall, at stated Times, receive for their Services, a Compensation, which shall not be diminished during their Continuance in Office.

Section 2
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;--to all Cases affecting Ambassadors, other public Ministers and Consuls;--to all Cases of admiralty and maritime Jurisdiction;--to Controversies to which the United States shall be a Party;--