There is mention in one of the chronicles, about the Imperial Navy. "Kiss of the Soul"
http://www.eveonline.com/background/potw/default.asp?cid=03-apr-01“This will not do.” The emperor said, his voice still strong despite his frail body. “I will not permit any military forces in space to be built or operated by anyone but the imperial navy. Allowing provincial governors to establish their own armed forces sets a very dangerous precedence that can only lead to future troubles.”
“The governors can have their ground forces, but I will not let them into space. The Amarr Navy will deal with this matter in due time. Need I remind you that the good of the whole empire comes before the individual lives of its inhabitants? Maybe I should make an example of one of you to refresh your memory.”
That was Emperor Heideran in YC105.
The House Navies, may be a loophole, or may be something else, depending on how strong the Imperial Law is, or the definition of military ships.
Police ships are not Navy ships, for example. Policemen aren't soldiers. Neither are security guards.
Could be Armed Merchant ships, heh. Just like how merchantmen carried guns because of pirates, in the age of sail. Just streeeeeeeetching the definition of "Armed Merchant Ship" a bit.
"This ship is a merchant ship, look it has a cargo hold"
"So I see. I also see it has 8 Tachyon lasers."
"Because of pirates. What is your point?"
Though, Uriam Kador's fleet contained dreadnoughts which would be a bit much. Illicit construction? who knows.
I think the only npc Amarrian dreadnoughts and carriers you'll see in missions are Imperial Navy (or deserters).
Amarr is, as always, complicated.
I think, the Imperial Fleet, would be raised and supported by Imperial taxation. Local forces would belong to the relevant House. When conducting operations, it would be the Navy commanding, with House forces acting as auxiliaries.
I would expect something like Navy battleship squadrons, with support from some cruiser and frigate formations, but possibly less cruisers and frigates than you might expect, with House cruiser and frigate formations to bulk up the forces.
So where the Gallente might deploy 1 battleship group, 2 cruiser, 4 frigates, the Imperial Navy would deploy 1 battleship group, 1 cruiser, 2 frigates and demand at least 1 House cruiser and 2 House frigate groups to support them.