Just to add my $0.02 to the mix, I usually play Advent and illum spam is definately something I do a lot, so I'll offer up what my fleet is usually composed of, as well as a response to some of the counter-strategies already posted.
My fleet is usually composed of (just to give an idea)
120-200 Illuminators
30-50 Defense Vessles (anti-fighter/bomber)
30-40 Guardians
20-30 Subjugators
Halycolon Carriers (Building Fighters only)
Mothership(s)
Battleships, late game
Personally I think adding at least 10 light carriers with fighters would strenghten this fleet considerably. Possibly lighten up on the subjugators to make room.
The principle adavantage of adding more fighters is to give the opponent some wild geese to chase. I still rely on flak to chew up opposing strike craft. This will prevent enemy fighters from targeting your Illuminators, no human will micromanage 70 fighters well enough, the AI won't even try. If you rely only on cap-ship fighters, the enemy will manage to shoot them all down and move on to target your frigates. With an extra 10 squadrons or so, you should be able to keep a few airborne at all times.
