How does the Galactic Federation Triumvirate work?

Hi, I've just finished reading the Legacy series and Legacy-War series comics and loved them, by far my favorite period in EU. I've gone through wookieepedia and can't find out how the GFT works. I know most hasn't been discussed but could someone give me their best guess or point me in the direction of someone attempting to figure the Government out? Like some of the questions I have are :
Does the military listen to the Emperor, the Supreme Commander, or the Triumvirate as a whole?
Are they divided between Alliance worlds and Imperial worlds?
Do the Imperial Knights command military forces, do the Jedi, are they shared? Stormtroopers still only loyal to the Empire?
So many more...

Any speculations would be appreciated!

 

I'm thinking it was more of an alliance than a unified government, kind of like the real world U.N. They agree on galactic laws and have a peacekeeping force, but other than that are still separate.

 

In my conception of it, the Federation was something of a cross between the UN as Meyerm suggests, and a constitutional monarchy. I figure the Emperor/Empress' power became more limited after the reign of Marasiah Fel, remaining head of state but otherwise an entirely ceremonial figure, with two Roman Republic-esque Consuls as joint heads of government taking the place of Supreme Chancellors/Prime Ministers (with far more constitutional limits on their power), and a ruling Council akin to the cabinet composed of the Consuls, Senators as well as the Jedi Grandmaster and so on.

The Senate or Congress would have an Upper House, composed of Imperial lords (mostly exceptional citizens such as esteemed academics or businessmen granted peerage) and nobility, and a Lower House of planetary representatives, working much as the House of Lords and House of Commons does in the UK. Thus would the Jedi, Alliance and Empire be satisfied in their government, greater planetary power (or power of lesser confederations such as the Hapes Consortiu) ensuring the Outer Rim is never disenfranchised again, and with the Jedi returning to their decentralised Tales of the Jedi roots, everyone lives happily ever after...