Data Centers are definitely split between the two; similarly, each of the AIs gets one Advanced Factory, Advanced Starship Constructor and Spire Archive. The fabricators, however, have all been owned by AI 1 - in this game as well as the last two, which didn't involve the Scorched Earth AI. I haven't checked to confirm, but my gut feeling is that a bunch of other special structures work the same way, including Zenith Power Generators and (less important, because you don't need to hold them) Distribution Nodes and Zenith Reserves.
Wow. You are absolutely correct.
There's 1 Fac IV and 1 ASC for each AI player (per human homeworld, I think).
However, all fabricators (Core, Exp, Starship) are on AI 1 planets.
All ARSs are on AI 1 planets.
All Broken Golems are on AI 1 planets.
All Dark Spire Vengence Generators are on AI 1 planets.
The Dyson Sphere is always an AI 1 planet.
AI Progress Reducers are generally split (Data Centers, Coprocessors, Civilian Leaders), however the SuperTerminal is always AI 1.
ZPGs, Raid Engines, Grav Drills, Planetary Cloakers, Armor Boosters/Inhibitors, Orbital Mass Drivers, and Ion Cannons all seem to be randomly distributed.
Yeah, AI 1 as a Scorched Earth would really be... inconvenient.