All I know is that they seem to have very distinct governments. Are they a separate nation from Noxus, Demacia, ETC.? There's no real maps of Valoran and I can't find anything saying they ARE a part of any preexisting nation.
Doesn't look like Zaun has it's own government to me, as it is more or less run by the Chem-barons who could equate to crime bosses/ councilmen according to their agenda. If anything I think Zaun is just considered Piltover's underbelly/ the slums of Piltover.
Piltover/Zaun are probably closer to a city-state than anything else. They probably have a couple satellite cities and exert influence on the isthmus that they inhabit, but besides that aren't technically a nation.
However, they are CERTAINLY not a part of any preexisting nation. Demacia would probably consider all of their hextech crafting to be unnatural and against the Demacian way, and Noxus canonically have plans to annex Piltover/Zaun. Leads me to believe that the Twin City isn't a part of any other nation itself.
Neither Zaun or Piltover really have a government. Individual dwelling and businesses are under the influence of specific parties (the Chem-Barons in Zaun or Bluewind Court in Piltover) but there is no party that is overtly in charge.
But they are indeed separate to Noxus and Shurima. Demacia is miles away.
There is actually a map piece where you can see where Piltover&Zaun are located. http://euw.leagueoflegends.com/en/featured/piltover/medarda-heirloom
They are pretty much surrounded by Noxus at this point and were originally between Noxus and Shurima until noxus conquered the northern shurima territories.
However since Noxus has plans to invade Piltover,we can be pretty sure that they are not an actual part of Noxus,so yes they are indeed independent(which is likely only possible thanks to their superior technology)
