There is a lot of elaboration that could be done on this topic.
We there is an Imperium government structure which is constituted by nobles, and is organized by subsector and sector. It has authority in starports, and over Imperium military installations and scout bases, and in space between planets. Except that planetary governments also seem to have some authority within their systems. If a murder occurs in in orbit of an inhabited planet, under what laws is the accused tried? If it occurs on another planet in the same system? Given that players do sometimes end up involved in matters that might or might not be murders, it could be important....
Then there are the nobles. They have fiefs, but are these extra territorial to the planets they are on? If so, are they under Imperial law, or under direct private governance? Perhaps, like medieval fiefs they have some kind of patchwork governance. I would be surprised if Imperial don't have a lot of authority in their own fiefs - so perhaps a degree of extraterritoriality - usually waived so as to keep good relations with the locals (as diplomatic immunity usually is), but it could be exercised if there is an important reason to do so. The nobles would need a staff - I would guess they have both a personal staff for their personal affairs - perhaps hereditary bonds of service - and also an Imperial government staff, overseeing the military, taxation, diplomatic and other matters. One can imagine someone unfairly accused of a crime might make a run for the Imperial noble's fiefdom, hoping to evade local law - and, if there is reason to give asylum - it could put the Imperial noble in a difficult political bind.
I think governance of subsectors and sectors would be separate from the fiefdoms, so paid for by taxes from the planetary governments, providing military, antipiracy patrols and ensuring free trade. Free trade is a lot more complicated than one might think. There are matters that it would need to handle, which relate to free trade, such as safety in shipping (if everyone has their own safety standards, governments start to use this as a way to interfere with commerce - if you can't stop the cheap goods coming in, you can stop the ships they are on). This gets into licensing of starfaring crew etc. Still, the government could be fairly limited, to standard setting. But what if it needs to deal out justice too (i.e. outside planetary government jurisdiction)? Then it needs a more developed legal system.
There might be conflicts of interest between what an Imperial noble's fiefdom's interest is , and the needs of subsector governance, which could result in interesting politics, possibly open, or possibly via hidden corruption.
It seems like the Imperium is a complex, multi-level polity with various centers of power. In this context, who rules a planet? is an interesting question without a straightforward answer.
