An example would be (purely because I read about them today, if there are notable other examples ease use them) the British king George III, who apparently also was "Kurfürst von Braunschweig-Lüneburg", a duchy in the holy Roman empire, and later king of Hannover. His wikipedia article says he never set foot in Germany, so did he get any taxes from these lands, did he decide any policies, did he ever elect an emperor of the holy Roman empire? Would he have if there was an election?
The other example would be Napoleon II, who, after his father had been banished was styled prince of parma and placentia and later duke of Reichstadt. Parma obviously is somewhere in Italy and he held no power over it, so did he actually get any taxes from them? Or was he entirely dependant on his mothers family giving him money? Was there a duke of parma or similar that actually controlled these lands? What did he think of Napoleon Franz calling himself that title?
Later Napoleon Franz's grandfather granted him the title duke of Reichstadt. Rheichstadt was controlled by his grandfather, but what did that actually mean? Did Napoleon from then on out get taxes from Reichstadt? Could he decide anything? If not, what might have been the motivation for his grandfather to even grant him this title?
Thanks for all answers!
This varies a lot by the time, the place and the nobleman/royalty.
The Hannovrians of Britain were indeed reigning Princes, later Kings of Hannover. However, they did not get any tax money from it. The agreement made with the Hannovrians was that the Hannovrian army could not be used outside Hannover and that any taxes collected in Hannover could only be used in Hannover. It was thus a net drain on the British monarchy, so why keep it?
It did offer several advantages. The British had a natural staging ground for any military operations on the continent. They also had access to the large supply of mercenaries in Germany - the King's German Legion and the Hessians being examples of such units that served the British well. They also had influence in the Holy Roman Empire (and later the German Confederation).
If the monarch or nobleman did hold land and right to tax or land rents, they would usually appoint a regent, caretaker or steward to manage the estates.
Karl X, XI and XII of Sweden was Dukes of Pfalz-Zweibrücken and appointed a Swedish governor (although the Duchy was under French occupation for some time during the reign of Karl XI) and revenue was sent to the Swedish treasury.
Titles granted prestige, and in the case of sovereigns, often a formal reason to intervene in wars and conflicts, since they in theory should rule the region they held the title to. Lots of monarchs retained titles long after losing all land related to it - the Habsburgs lost the castle of Habsburg in 1415 for example.
When creating higher nobility, it was common to give them a pension or allowance of sorts, a yearly stipend that in theory would be partially from the estates of which they gained the title from, but in practice often came directly from the income or the state coffers of the one who created the title. The actual land would continue to be part of the state owned land of the creator of the title.