How and when does Oxygen (O2) detach from haemoglobin in the Capillaries? 

The process involved is called The Bohr Effect.

This whole process is responsible for the detachment of oxygen from Haemoglobin in the capillaries. In the pulmonary artery capillaries,the oxygen (O2) combines with hemoglobin (Hb)to form oxygenated hemoglobin.

And, at end-organ capillaries, the oxygen dissociates from hemoglobin due to the lower pH, higher pCO2, and temperature. The whole process can also be depicted by the oxygen dissociation curve of hemoglobin.

The detachment of oxygen from Haemoglobin in the capillaries is a result of the Bohr effect. This effect is responsible for extremely efficient oxygen system delivery in our bodies. At first, Oxygen combines with Haemoglobin to form Oxygenated Haemoglobin, In the end, the increase in CO2 partial pressure in the blood contribute towards the lower amount of Haemoglobin in the oxygen.