The FOA own a BAe 146 which Bernie flys about in to all the races. The FIA dont own any aircraft they just charter them. They require four 747's to carry all the digital tv equipment around to fly away races, in Europe a fleet of special trucks are used. The teams sometimes have agreements with individual airlines, Japan Air for example for the team i work for. But most of the time they we all grouped together and who ever can supply enough aircraft gets the job.
Veni, vidi, vici.