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ost_uid0]This is one of those questions kept vague so the writers wouldn't paint themselves into a corner. After TOS ended, it was bandied about that there were only 12 Constitution-class starships, and much fan speculation has gone into assigning names and registry numbers to them.
I think the apparent size of Starfleet ballooned at the end of DS9 for two reasons: the script called for it, and advances in CGI technology made it possible to show more than two ships travelling in tandem. As to how many ships Starfleet really has, I have no idea. There are at least three Fleets mentioned by name (3rd, 7th and 9th, the latter getting wiped out in the opening arc of the sixth season). A Fleet seems to consist of about 2-300 ships. Whether there are really nine (or more) Fleets in service depends on whether Starfleet started numbering their Fleets at 1 for this war, or continued the numbering scheme from a previous war (this has at least once precedent in Earth history that I can think of, and probably dozens more that I'm unaware of).
As to what ships count towards the total...the US Navy counts ever landing craft, supply ship and tugboat towards its combat strength, so the current fleet of 400 or so ships is about 75% unimpressive scow.
I've just had another thought...the other reason Starfleet was able to increase its numbers so fast was that it didn't bother installing armour or shields on anything except the Defiant. This can be seen in any battle scene: the Defiant takes dozens of hits, consoles explode and spray sparks, but the pristine white hull is undamaged. The Miranda-class scow escorting the Defiant takes a glancing blow and is instantly converted into plasma.
I dunno if this any of this clarifies the issue or confuses it, but it's my .02 credits worth. There are websites out there that speculate as to the size of the Federation (but the names escape me) and also attempt to reconstruct the design lineages of the ships we all know and love. The latter is called the Starfleet Museum, or something. There's a link of
Ex Astris Scientia This is an excellent fansite. It puts a lot of rational thought and effort into speculations, and manages to spell all the words correctly as well.[/color
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