The RT game is focused on 'young' Trader dynasties with no tangible resources outside the Koronus Expanse. But what about 'established' dynasties? The 'name' NPC dynasties operating in the Koronus Expanse have probably brought several planets into the Imperium before venturing into the KE (it's reasonable to assume that the Winterscale dynasty, for instance, discovered several worlds within what became the Calaxis Sector).
So, my question is, what connection do the dynasties retain with the planets they discovered which have subsequently become 'standard' Imperial worlds? Do the dynasties continue to 'administrate' these worlds under the eye of the Sector government, or do they turn them over wholesale to be governed by officials appointed by the Lord Sector? Do the RTs continue to draw revenue from the worlds their dynasty discovered even after it becomes Imperial property? If so, how? Do they receive a tribute raised by the world, or do they get a percentage of the Imperial Tithe? In perpetuity?
Sticking with the example above, let's say the Winterscale Dynasty discovered a Mining World in the Calixis Sector before relocating to the Koronus Expanse- what connection, if any, does the dynasty retain to this world now that it is fully a part of the Imperium?
Note that I'm asking about color description, and not 'crunch'.
My interpretation has always been that once a planet has been brought "into the fold" and have grown to a certain size, it becomes tithed by the Administratum. This process can take centuries, depending on where the planet is, how it was brought into the fold, and whether the secretary was sick that day or not.
At about this point, it should also receive an Adeptus Arbites precinct/courthouse and be required to raise a Planetary Defence Force of some kind or another. This is not a given, though, and exceptions apparently exists.
This tithe is usually a matter of fact kind of deal. Some planets Tithe gold, other planets tithe people, some worlds tithe plants. Who rules the world and how it ruled in general, the Administratum does not seem to care overly much. The Sector Governor might have some say in who becomes the Planetary Governor, but overall, who becomes Planetary Governor seems to be mostly a matter of de facto, rather than an issue of de jure.
As such, I'd expect the Rogue Trader Dynasty to have quite some say in who rules the planet as Planetary Governor, and how that rule is exercised. They conquered it, discovered it or otherwise brought it into the fold, what they say, goes. In the labyrinthine connections of the feudal structures of the Imperium, there may be a laundry list of conflicting interests that might have a say, such as the Imperial Guard and Navy claiming it's necessary as a staging ground or Fortress World, or a Sector Governor directly assigning his nephew as the Planetary Governor, or something like that, which could surely be contested in one way or another (such as a Dynastic Rogue Trader's position as a Peer of the Imperium).
So, on the question as to whether a Dynasty would remain 'in control' of a planet even after it's being tithed?
The short answer is yes.
The long answer is maybe.