Regarding Nazi Germany, let's say, it's complicated. While it's true that Hitler apparently envisioned a corporate society in "Mein Kampf", in actuality, the industry was much more structured capitalist than anything else, even in WWII. Thus, corporatist tendencies merely controlled the labor force and bound the intellectual class and educational system to the state, rather than actually defining the economic system. (This is also true for Austria, which was an explicitly corporate state in the 1930s before the Anschluss.)

Edit: As far as economic theories of the "Third Reich" are concerned, there was (quite naturally) a fascination with Fordism.