Jacko,
My understanding (which could well be wrong) is that air superiority can be a temporary thing. An example - when a huge package is going into the badlands, the F15Cs clear out the red air, and provide air superiority for the period while the muddies get on with their work. However, when the package all goes home, then the enemy still has fighters etc that can cause problems at a later time.
Air supremacy is the next step up, when you've wiped out most of your enemy's air force and they're only capable of throwing up the odd aircraft to cause the occasional nuisance.
Air dominance is when they have nothing left, either in terms of airframes, or the 'will to fight'.
So in the Iraqi context, you might say that during Op Southern Watch, the coalition had air superiority in the southern no-fly zone during a 'vul' period, but perhaps not 24/7. During the opening days of GW1 the coalition had air supremacy, but the odd Iraqi still got airborne. During Iraqi Freedom though, with the Iraqis burying their aircraft, and when I don't believe a single one got airborne, you'd say that the coalition had air dominance. It's all in the nuance of the level of 'interference' the enemy can or does cause.
A favourable air situation would be one when the enemy are still coming up in numbers for a fight, but you can get the job you're trying to do done. eg Korea in Mig Alley perhaps.
I might be totally wrong of course, and ready to stand corrected by the doctrine gurus out there, but that's my take on it.
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