A word or two about shadow placement with the Zone System:
Blindly placing shadows in a given Zone, be it II, III, or IV or whatever, isn't taking advantage of the visualization aspect of the Zone System at all, and which is its major advantage, IM-HO. That's equally as misguided as simply rating your film slower because someone says it's a good idea.
The relationship of D-max (maximum black in the print) in conjunction with the look, feel and texture of the shadow value you are placing is a first primary concern. Then, it's how you want any particular shadow value rendered. I place some shadows in Zone II (when I want a dark, featureless, black that still has some feeling of "reality" in the scene, not just a massive black patch) and some in Zone V (luminous shadows in snow are great here) and some in Zones III and IV, all depending on what I want the shadow to look and feel like.
The first part of the above, the relationship of a particular shadow rendering to D-max in the print is a function of exposure. Not enough exposure and you won't get enough separation between maximum black and Zone III, for example and the whole scale gets skewed (note that overexposure, to a point, isn't a problem here). Note that the way Zone-System metering works usually results in the film being rated 1/3-2/3-stop slower than box speed. Still, one should test, keep notes and refine their personal E.I. to give them the desired max-black-to-shadow-value relationships.
The second part of the above, how you visualize and place a shadow in relation to the other tones in the scene, is the crux of the visualization part of the Zone System. Shadow values have expressive qualities and where you place the shadow in a scene has a lot to do with the expressiveness of the print. (Highlights get taken care of with development/paper-contrast choice). Mindlessly placing all shadows in the same Zone because that's what the "system" says to do for proper exposure is a misunderstanding of the Zone System.
Best,
Doremus