How is owning faction selected for new facility?

The last couple of facilities I've built have gone to the faction with the third highest influence. Is there a way to get new facilities to be assigned to the system controlling faction from the start, so I don't have to do BGS gymnastics to get the new facilities to be owned by the faction I want (which currently is the system controlling faction)?
 
The last couple of facilities I've built have gone to the faction with the third highest influence. Is there a way to get new facilities to be assigned to the system controlling faction from the start, so I don't have to do BGS gymnastics to get the new facilities to be owned by the faction I want (which currently is the system controlling faction)?
I guess they want a balance of faction owned assets, not all belonging to one which would make for rather dull BGS gameplay.
If the second and third factions have a certain percentage influence it makes sense there should be a random dice roll to decide ownership when something is built, with the influence as the chance of that faction gaining the asset.
As "just the architect" we shouldn't decide on the balance of political power anyway.
 
It's not completely clear - random, but with a bias towards the higher-influence factions, seems likely.

It seems intentional to try to specifically prevent (or at least, make it a deliberate choice to achieve) single-faction ownership of everything in the system.
 
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