This is slightly related to my other question on variable-pitch controls.
I want to know if WW2-era aircraft typically had variable-pitch or constant-speed propellers. Variable-pitch lets the pilot adjust the propeller blade pitch. "Constant speed" is the same as variable-pitch, but the engine does it automatically to keep the best performance at various airspeeds. This also lets the engine keep a constant RPM so it can always run at its optimal RPM, also increasing efficiency.
Anyway, were such things seen in WW2? Were they the norm, or the exception? Did single-engine aircraft have them, or were they more common on multi-engines?
I'm interested in all the nations who made aircraft, especially USA, UK, USSR, Germany, and Japan. And I'm interested specifically in the combat aircraft, like fighters and bombers, not necessarily the civilian transports of the era. This will give us a good idea if the extra complexity and weight was acceptable for combat aircraft of the era.