It's kind of eclipsed by when we actually meet him, but we heard about Cartagia for a year and a half before he finally showed up on-screen. The upshot seemed to be that he was Refa's puppet and public face, and once Refa was dead, Cartagia took no time at all going from "uncontrolled" to "out of control."
"The Coming of Shadows" had Refa introduce him this way; "And the unfortunate death of the Prime Minister so soon after the emperor has had the effect of tilting the balance of power back home. Several competing families
have been neutralized leaving the Emperor's nephew to claim the throne. A young man who feels as we do about the future. For the first time in a hundred years, ambassador, our people are on the right track again. And we have you to thank for it. You will find the new Emperor's gratitude most rewarding."
And then in "The Long, Twilight Struggle," Refa said, "[Cartagia] is out among his people, basking in their almost-sincere adulation." And then in "Ceremonies of Light and Dark," Londo doesn't make any bones that Refa is the one telling Cartagia what to do.
It's possible Clark was a similar puppet-turned-master, given the hints that he was connected politically to the Psi-Corps. Bester's wing of the organization probably would've been happier with a Vice-President whose influence they could benefit from but who had no real power in and of himself, and their own aims were probably disrupted by the Shadows killing Santiago and giving Clark actual, unlimited power instead of remaining under their thumb.
And, come to think of it, the Shadows also orchestrated Refa's assassination. I always wondered what the deal was with that; they never seemed to get anything out of Londo un-divorcing from Morden and calling in a new favor, he didn't even to seem to need Morden's help with killing Refa, but what if the "favor" was what they wanted from Londo? Their longer-term plan was getting Cartagia off the leash so he would flail and self-destruct and plunge every nation bordering the Centauri Republic into endless quagmires, and Londo cutting Morden off and then forcing Refa to do the same was a setback. It'd be consistent with the Shadows' M.O. to have the ultimate goal of having the most irrational, id-driven people possible in positions of ultimate power in the younger races; they'd start more wars, stir up more conflict externally, and then the same thing would happen internally, as even the Vorlon-esque structures of government, military, and society had to resort to conspiracies, coups, and civil wars to defeat their own self-chosen leaders.
