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Mechanized What was the mechanized/motorized distribution in German Panzer divisions?

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Mechanized/motorized distribution in German Panzer divisions

I've read a lot of organization charts for German Panzer divisions. In most of them, they have one panzer (tank) regiment, one artillery regiment, two or three panzergrenadiere (mobile infantry) regiments, and various support batallions (AA, AT, engineer, recce, etc).

This question is about the panzergrenadiere regiments. Most charts only denote them as "mobile", and that they could be either mechanized (i.e. with armored halftrack transport) or motorized (unarmored truck transport).

Given the difference in (offensive) combat value of mechanized and motorized infantry, I'm curious about the relative amounts of them... some sources indicate that only a single battalion, or even company, was mechanized, and all the rest was motorized. Could this be true? With such a low mechanized proportion, how did they get their effectiveness and legendary status in the early stages of the war?

To a lesser extent, this question is also about the artillery regiment... how much of it was self-propelelled (e.g. Wespe/Hummel) and how much of it was simply towed?