Is there anything common about the systems that they have been discovered in?
i.e. Do all of them have Ammonia atmosphere planets, or waterworlds, or earthlikes?
What is the distance from the star at the point you recover them? Is there a "goldilocks zone" for UA?
Noting that Bast has also had plague, are there any correlations with plague outbreak, the UA and inhabited worlds (i.e. Earthlikes) and large populations. Are they appearing only at large pop systems?
Is there a correlation with regards to faction, political allegiance or the like - are they only appearing in areas supported by one power/major faction?
That little table above might be worth expanding with allegiance, distance from star (where available), number of earthlikes, num waterworlds, num crazy ammonia planets maybe?
From that point, could we put together a predictor of where some MIGHT be in the vicinity and test the theory?
Poeple have seen no commonalities, they might not have looked to the level of detail you suggest though, maybe collate and add in the data?
They have been sighted in Federal, Imperial and Independent systems.
It's said they appear in "deep space" only, but that could just be a self-full filling prophecy sort of thing, someone thought that once, so that's where everyone looks, so that's where they're all now found etc...
For me the Bast link was just that there was a high SSS rate, which could just have been down to it being increased due to the plague CG. Also a lot of people were at Bast hence bigger chance of a sighting, so people descended on it and again more sightings, again these things are almost self-fulfilling. Someone thinks there may be a link, so people go there, so a few UAs are found, which then reinforces the link, when in reality there may be none.
The trouble is the rarity combined with the RNG makes it incredibly difficult to prove anything as regards a spawning pattern. All you can do really is find an instance that does not match currently thought criteria for finding a UA, but who is going to spend 100 hours camping somewhere where it's thought a UA probably won't spawn? And then at what point do you decide they cannot spawn there? 2 weeks? Even 3 weeks is not enough. =(