David,
I have tended to look at the application and available equipment to dictate whether division of the dough should take place before or after the bulk rise.
For example, for a room temperature application such as Marco (pizzanapoletana) advocates, and where two fermentation stages are deemed mandatory, I would do a bulk rise and then the division into individual dough balls. This gives credence to the two-stage process that Marco says is necessary, but it also acknowledges that it is easier to divide a warm dough in bulk into individual dough balls and to reshape them into a nice round shape in preparation for the ensuing several-hour maturation/ripening stage.
For a dough that is to be cold fermented, I would advocate doing the division up front. Otherwise, it can become difficult to try to do the division of the bulk dough while it is cold and to be able to reshape the individual cold pieces into nice round shapes, especially if the tempering period is too short to allow the gluten to relax sufficiently to overcome the increased elasticity from rehandling. The objective here is to minimize handling of the dough while it is cold and somewhat intractable. I have seen instances where cold fermented dough balls are reworked by hand to achieve a better gluten structure but doing so requires planned intervention and may limit how soon the dough balls can be used. Most commercial operators prefer to make the dough balls up front, put them into the cooler, and use them within a few days after a brief tempering time.
In situations where a roller/sheeter is available, then it doesn't matter as much whether the division is done up front or later. It also doesn't matter as much whether the dough has been cold fermented or not. Moreover, the shape of the dough is less important; a piece of dough cut away from a bulk dough can be run through a roller just as easily as a dough ball that was formed in advance. I have seen applications where bulk dough is sheeted into skins and then put into the cooler for later use (Monical's and the early Pizza Hut fresh pan doughs), or where pieces of dough fermented in bulk in the cooler are run through a sheeter and formed into skins (e.g., Round Table and early Donatos), or where individual cold fermented dough balls are run through a roller and formed into skins (e.g., Giordano's). There are also places that ferment a dough in bulk at room temperature and then run pieces through sheeters as needed to fill orders. In general, pizza style is not a limitation. Just about any style of dough can be run through a roller/sheeter, although the most common tend to be the cracker-style, thin style, deep-dish style, and pan style doughs. NY, American and Neapolitan-style doughs are shaped and stretched by hand for the most part.
Peter
