On the scale of the typical MTW battlefield, I generally don't split forces, but there are exceptions, and it really boils down to specifics of a particular battle... as ever, universal 'rules' don't apply

And of course it depends on faction, army composition etc. With a strong HA faction (like Turks) then I might have a forward wave of HAs to break up the enemy formation before the tough guys get in there... and the classic hammer/anvil will always have a place, but whether that really counts as 'dividing' your forces is debatable, as it's a tactical application of the 'march divided, fight united' principle.

In double bridge battles a few cavalry units running between the bridges can be a great tactic as the enemy runs from bridge to bridge whilst your archers are ranged along the bank between bridges. But that's evil....