Dominion takes Shirow's love for police stories and gives it a thoroughly comedic twist, poking fun at whatever Shirow feels like. This is a highly amusing read that I recommend to anyone when they're looking for a break for all those mopey, serious police/mecha dramas like Patlabor. As you can see below, it was released in three segments - Dominion proper, Dominion: Conflict, and the Phantom of the Audience one-shot, with the possibility of more if Shirow ever finds the time.
The original, a 6-issue series following Leona Ozaki and the rest of the Tank Police, a special branch of the police armed with, you guessed it, tanks as they try to put a stop to the rampant crime in their city. In addition to the nonstop criminal activity, citizens also have to worry about the deadly bacterological cloud covering the planet, which was caused by mankind's mistreatment of the planet(of course). Key to the storyline is criminal mastermind Buaku and his twin catgirls, Annipuma and Unipuma, who are constantly causing problems for the Tank Police to deal with in rather comedic fashion, as tends to be the tone in Dominion.
Subtitled No More Noise, this sequel to Dominion, another 6-issue work, picks up a little bit after where the first series left off. As it is a sequel, I really can't say a whole lot about it on the overview without spoiling things. Leona still loves her little Bonaparte, the Tank Police continue to demolish the city in pursuit of crime, and the citizens are near the breaking point with all the destruction, imposing new laws, regulations, and the like upon the Tank Police. Unfortunatley I can't comment on how this one begins, as I only have issues 2-6, and have never seen the first issue anywhere, nor have I gotten ahold of the collected version to substitute for it. Additionally, the covers below indicate that this is part 1 of Conflict, but to the best of my knowledge, part 2 of Conflict doesn't exsist as anything more than possible sketchwork in Shirow's house, another project that sits on his backburner along with Appleseed 5 and Neurohard.
A one-shot special that Shirow did, it comes into the timeline somewhere between the initial Dominion manga, and the Dominion: Conflict follow up. While it is currently rather hard to track down in its issue form, it has been added into the 3rd Edition of the collected Dominion trade paperback, along with some character bio pages, which is where I know it from. As far as I can tell, the title has very little to do with the actual plot, unless I've missed something. Essentially though, Leona and the Tank Police are called down to keep a pile of protestors from rioting against a public official who runs a sport that regularly kills some of its participants.