By deep I mean like what you see in films. Enemies all mixed in with each other and no lines. So Gladiator, start of Lincoln, Braveheart etc. Obviously with phalanxes and shieldwalls the soldiers would only fight at the front but I'm wondering about all other types. Thanks!
Drawing from the description of Punic Wars era warfare in Adrian Holdsworth's "Fall fo Carthage"
Generally combat between two organised armies in battle order was carried out in width for short periods of time. Units would periodically disengage and retreat several paces to get a breather before launching back into the fight. However the depth of the formation was still important, as this affected the effective mass of the formation that could be leveraged to push through the enemy. Push hard enough and you would be able to break enemy lines, often causing them to either rout or be encircled.