The German air contingent in North Africa was "a detachment of Fliegerkorps X". The commander, General Geisler, was based in Greece. His main concern was control of the sealanes and the war at sea. In November 1941, Field-Marshal Kesselring took overall command, with Fliegerkorps X as part of his Luftflotte 2. The commander in North Africa, the Fliegerführer Afrika, Major-General Frölich reported directly to Kesselring. Rommel was not in Kesselring's control and the Italian air forces had their own command structure.
In contrast to the undesirable Axis air command structure, Air Marshal Tedder, commander in the Middle East, had every available squadron in the Desert Air Force under Air Vice-Marshal Coningham's command. Coningham was co-located with the 8th Army HQ and worked closely with the army commander. He had achieved air superiority for the duration of the Crusader Battle, and that greatly affected the outcome of the battle.
This is based on the account in Vol.III of the Official History.