Luftwaffe replacement aircraft system (?) 1940

How did Luftwaffe units replace lost AC in 1940?

Up till now - possibly partly for lack of time, for I own two books on German aircraft PRODUCTION - I don't really know how Luftwaffe combat units - bombers, recce, fighters - replaced their lost aircraft (destroyed or badly damaged, hence for a while not combat-worthy).

When reading various books of German origin I got the impression that combat units had to fetch replacement AC directly from the tarmac of the factories and there were no suply pools (like in France, where they contained many hundreds of aircraft, new ones or "second-hand", and, it seems, in the UK) - reserve pools between the factories and the fighting units. It seems the LW did have some ferry pilots do deliver AC to the units. The famous provisional registrations on the sides of the fuselages, in big letters, seem to be explained by this system (French AC got their definitive markings directly within the units but possibly the "matricule militaire" on the lower side of the wings was applied in the factories). 1940 (and 1941) German production was much too low so obviously they couldn't afford to "lose" any AC in reserve pools feeding the units, they had to use the "straight (tense?) flow" system, which nowadays is so fashionable within industry. Are these assumptions correct?

(An example : 1940 Germany produced about 142 Me 109s monthly on average, France produced about 200-300 fighters monthly and would have reached 500 in September and 620 in November, in August 1940 the UK did reach 500 per month so clearly the German fighter units must have been very eager to lay their hands on any 109 they could get. Germany could not win 1940 even if lack of aircraft - bombers too - had been the sole reason).

Fighter deliveries were strongly boosted in France in May and June 1940 but, perhaps not surprisingly, in Germany too : in France 296 new fighters in May and 331 in June, in Germany 195 in May, 230 in June (then deliveries fell back). (French source : Danel and Cuny : Docavia-book on French fighters; German source : J. Prien IIRC).

Was there any "fighting" about replacement aircraft between various Geschwader and Gruppen actually? Were some Kommodores, possibly Galland, better at this business?