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Since SCII happened 4 years after SC BW, how much technology, military, economy, etc has UED improved? Maybe UED too busy colonizing other planets that they found in different sector of galaxy. Not like UED only has Earth.

That is probably the most likely. (Not necessarily colonization though) The UED realized that it would take more to get rid of the alien threats...but those alien threats are too far out to worry about.

I could see them returning with a much bigger force in SC3 (I doubt they would play a role in LOTV)

I bet the UED change there name to the imperium of man , made war with other aliens, and was just too busy to dell with the terrans, protoss, and zerg.

but i'm just making this up

it would be cool seeing the warhammer 40k universe and starcraft universe john like that

I am happy to see players who have played sc1 or read the sc1 storyline. In the Brood Wars expansion, you get to play 10 levels as the UED and lots of crazy plot twists happened. According to the reccent Q&A lore, the UED is not 100% destroyed; there are bits and pieces of that military force.... even confederate forces!.

I love the sc2 lore and I hope to share. What I am currently doing is working on 2 custom maps - Desert Strike Broodwar and Desert Strike Night. Each of them will bring back.

[Spoiler Alert of my maps]
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Desert Strike Broodwar will be a hybrid map of Nexus Wars and Risk. Players will instead of choosing the usual 3 races, they will be able to choose 1 out of 9 factions.

Sons of Korhal
Confederates
United Earth Directorate
Overmind forces
Kerrigan Swarms
Cerebrate broodlings
Tassadar Fleet
Zeratul templars
Fenix legion

I will bring back old extinct units such as the Reaver, defiler, valkyrie, dark archon, corsair, dragoon, terran dropship, shuttle, arbiter, flying queen and fast-infested-baneling-killing-terrans.

Fors
The closest thing you're going to get to the UED in SC2 is the Spartan Company mercenaries.

Though in the wider lore there is the possibility of Stukov starting something up. It would be cool if he joined Raynor, imo.

He's dead.
He shot himself, and later Kerrigan turns his body into infested terran I think.
That's what I read in a book