Lets just say its like a civ without a city that uses the corruption of a city to fuel its efforts and produces its stuff in that same city. Also, what kind of things this civ builds and researches are different. This means that corruption does nto disappear, but accrues somewhere. This also means having a lot of corruption can lead to more problems than now where it just makes a failed state.
Types of Corruption:
Trade - This trade would be distributed according to your current tax rate.
Culture - This would be calculatted roughly the same way as trade and would go to the local entity.
Shields - This would go towards local entity buildings and units.
Food - This food would still contribute to the growth of the city, but over time as citizens are 'birthed' by the corrupted food, they are really just converted from Greeks to Delphians.
Purpose of (blank) to local entity:
Gold: Pays for maintenance of militia and local entity buildings.
Beakers: Contributes toward 'local' research. These techs give local buildings, militia units, and possible demands.
Happy Faces: Can only be used for local citizens.
Culture: Thresholds allow for construction of certain buildings and certain demands for greater autonomy.
Buildings: Some generate more local culture, others allow for certain demands, others allow for building of certain militia, others provide bonuses to the city(like library or bank, etc.).
Militia: These are units that stay in the city for the purpose of defence or a possible secession.
Local Citizens: Having a certain number of locals vs. nationals will lead to the ability to make certain demands. Also, they gain happiness from appeasement and are mad from the opposite.
Dealing With The Local Entity
You will be informed about any buildings being built and units that have been trained. If need be, you can order the disbandment of militia or the destruction of buildings. Disobedience can be answered with military force, although some other nation may choose to champion the upstarts.
Over time various cities will come to you with demands for greater autonomy. You basically have three options to deal with these demands. 1) Appeasement, 2) Ignore, 3) Punish. Ignoring the option will generate frustration but not hatred. Punishment will usually lower clamoring for a while, but is a dangerous road for the future. Appeasement has the disadvantage of allowing the city to become more local. Over time though, if you can keep a good city appeased and still part of your civ, you can generally gain a lot from unique local structures.
Punishment is probably a good strategy for colonies or the edges of your empire, where you little in common culturally.
Secession
At some point a city may decide you have not appesed them enough and they want to govern themselves completely. One city nearby will raise local cities desire to secede, especially if they have not been well appeased. Usually in a volatile region many cities will secede at the same time. They usually unite behind the city that seceded first. If the first couple of turns go well for the turncoats then other cities might join as well, or form their own alliances.
Civil War
A powerful city may be loyal to your civ culturally, but desire control. They will usually convince nearby cities to join them. Depending on how the civil war progresses, cities may strat abandoning the current leadershp. A viable tactic against enemies would be to find disloyal cities and encourage an uprising, maybe even funding or supplying arms.