I believe by talking about depth of breathing you are talking about tidal volume (TV).  This is the measure of the amount of air moved in and out of your lungs during a single breath.  During normal activity, the average tidal volume for a person is about 500 milliliters.  When exercising, there is an increased need for oxygen by your cells and also there is an increase in the amount of CO2 that you need to expel.  So during exercise a person's tidal volume will almost double to about 1000 milliliters (1 liter).  In highly trained athletes, tidal volumes can reach up to 2 liters.