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Thurn und Taxis is a German princely family most famous for starting the first modern postal service. Wikipedia lists the County of Thurn und Taxis as a state of the Holy Roman Empire in the Electoral Rhenish Circle, but it isn’t clear where exactly it was. So where was it located in the empire? Or was it not landed?

Nowhere. As at the time they were introduced to that circle, they were not landed.

The family Tasso originated in Lombardy and made up their genealogy to include "were once rulers there". While the Rhenish Circle consisted mainly of territories, represented by their rulers, the Thurn und Taxis family were personal members of that circle.

This was compensation for the debts the emperor had with them. An exception; and quite vigorously opposed by the other, traditional, landed rulers.

Also note that

Wikipedia lists the County of Thurn und Taxis as a state of the Holy Roman Empire in the Electoral Rhenish Circle…

is not the correct reading for this. Wikipedia lists them as members (and unlike the correct German Wikipedia, the English Wikipedia confuses readers with the table heading "states", while correctly grouping "Type of entity: Barons –– Briefadel without territory, Freiherren from 1608, Counts from 1624, raised to Princely Counts in 1695"

Cornello dei Tasso at Camerata Cornello, Lombardy
The Lombard dynasty first appears in documents with Reinerius de Tasso in 1117. Odonus de Taxo is mentioned 1146 in Val Brembana, north of Bergamo; there the name also appears around 1200 in Almenno. During the battles between Guelphs and Ghibellines in Bergamo, between the Colleoni and Suardi families, the family moved to Camerata Cornello, a few kilometres higher in the valley. Here, with Homodeus de Tazzis (Italian: Omodeo de Tassis del Cornello) in 1251, the line of the tribes begins. The hamlet of Cornello dei Tasso still reminds us of the family.

Tasso is the Italian word for badger, the heraldic animal of the family, Dax, Daxen, from which the name Taxis developed. In the French-speaking postal contract of 1505 between Philip the Fair and Francis of Taxis, the de Tassis family was named, as is still customary in French today.

Thurn

When the Taxis, which had meanwhile moved to Brussels, were elevated to the status of hereditary counts in 1624, they needed an illustrious ancestry to legitimise their intended advancement to the high nobility. Alexandrine von Taxis commissioned genealogists to "clarify" the origin of the taxis, which until then had only been regarded as a small family of knights who had changed to the merchant class. They now claimed, albeit without documentary evidence, that the taxis descended from the Italian noble family of the Torriani, or della Torre, who had ruled in Milan and Lombardy until 1311. As a result, the taxis applied to the emperor for a change of name. During the Germanization the tower (Torre) became Thurn (cf. mhd. turn) and the tower was added as coat of arms multiplication.

Thurn and Taxis

From 1650, with the permission of Emperor Ferdinand III of Thurn, Brussels taxis were allowed to call themselves Valsassina and Taxis, which became Thurn und Taxis, in French de la Tour et Tassis, in Italian della Torre e Tasso. Also the Innsbrucker and the Augsburger branch of the family renamed themselves.

The early ennoblement wasn't all there is to it:

In 1681, the Brussels line (later in Frankfurt and Regensburg) was elevated to the Spanish-Dutch princely estate with Eugen Alexander, with Braine-le-Château as Titular Principality (Principauté de la Tour et Tassis), and in 1695 to the Imperial Princely Estate, although at that time no territorial possession existed in the Empire. In 1704 he was admitted to the Imperial Princely Council, with a share of the Kuriatstimme of the Kurrheinischen Kreis at the Reichstag; in 1724 he was admitted to the Schwäbisches Reichsgrafenkollegium for Eglingen; in 1754 he received a Virilstimme for the Reichsgeneralerbpostmeisteramt; in 1803 he received another Virilstimme for the Reichsfürstentum Buchau. Since 1741 the house on the "Perpetual Reichstag" has been the principal commissioner.
_{(Translated from Wikipedia Thurn und Taxis)}

So the princely house Thurn and Taxis was 'an estate' of the Kurrheinischen Circle, but did not possess a plot of land in the same… (src)

This is not to say that they didn't have any territory under their control, despite having a clear centre for their lives in either Brussels or Frankfurt when they entered the Kurrheinische Reichskreis. The full title of Karl Anselm von Thurn und Taxis (a mere century later, 1733–1805) was

Des Hl. Röm. Reiches Fürst zu Thurn und Taxis, Graf zu Valvasina, Freiherr zu Impden, Herr der Freien Reichsherrschaft Eglingen und Osterhofen, Balmershofen, Durtenstein, Wolfertheim, Rossum und Meusseghem, der souveränen Provinz Hennegau Erbmarschall
_{Michael Müller: "Die Entwicklung des Kurrheinischen Kreises in seiner Verbindung mit dem Oberrheinischen Kreis im 18. Jahrhundert", Peter Lang, 2008. (p 126–129)}

The point here is that none of their lands where within the Reichskreis and those lands they did own at the end of the 17th century were private property, not princely estates eligible for being a member of a Kreis.