There were two central guidelines that undergird the German occupation of Greece. One, the Germans wanted to maximize whatever strategic benefit they could derive from the occupation of Greece. The country was marginal in German strategic planning prior to 1941 and the German military and civilian agencies constructed much of the occupation policy on the fly. Second, Hitler and the Wehrmacht were determined to accomplish their first goal with as little German troops as possible. These two slightly contradictory, but reinforcing, goals contributed the the divided occupation zones for Greece.

In the case of Bulgaria, Hitler allowed his ally to occupy Greece's larger wheat-producing areas. This was of a piece with Hitler's other policies in the Balkans which rewarded his minor Axis allies with slices of conquered territory. Italy received the lion's share of Greece because Hitler had sanctified this area of SE Europe as falling within the Italian sphere of influence. Nonetheless, Macedonia/Thrace was too important to leave it just to Bulgaria. The Germans created a buffer zone of their own occupation at the Turkish border as well as occupying the northern Aegean islands. This was a threat to Turkey that would be used to guarantee its friendly neutrality towards the Axis lest it fall to Allied overtures. One of the lessons the Germans derived from Operation Marita was that their Axis allies were often not up to German standards, thus there needed to be a German military presence.

This low estimation of its allies was why the Germans were determined to hold onto Crete and keep a small military force in Attica. Crete was designated a Festung (Fortress) and the Germans saw it as one of the linchpins for Axis (German) security within SE Europe. The Italians had a small Cretan occupation zone partly because Operation Merkur was a joint Italian-German operation- the Regia Marina did try to land German troops- but also because an Italian occupation zone would be bureaucratically connected to Italian Rhodes. This would allow the the German garrison access to food and other resources from the Italian Dodecanese.

In practice, the German administrative plans for occupied Greece did not quite work out as planned. The rewarding of minor Axis allies with Greek territory did not sate them or make them more reliable allies. Instead the division of Greece only heightened bureaucratic dysfunction and infighting among the nominal Axis alliance. The Aegean may have been a small-scale theater compared to the Eastern Front, but it still demanded a degree of German attention. The presence of German armed forces on their border in Thrace, and after the Italian capitulation, the Dodecanese, may have helped keep Turkey neutral. But Turkish neutrality was something that Ankara was already predisposed towards when the war's outcome was uncertain. The Germans may have wanted a cheap Greek occupation that derived maximum benefit for Germany, but this was easier said than done.

Sources

Mazower, Mark. Inside Hitler's Greece: The Experience of Occupation, 1941-44. New Haven: Yale University Press, 2001.

Militärgeschichtliches Forschungsamt. Germany and the Second World War, Volume V: Organization and Mobilization of the German Sphere of Power. Oxford: Clarendon Press, 2000.