"S" shaped:- at a low partial pressure, haemoglobin has a low affinity for oxygen because it is hard for the O2 molecule to reach the haem group in the centre of the blood cell- when partial pressure rises, the diffusion gradient of oxygen into haemoglobin steeply rises, when one oxygen molecule has bound to a haem group the haemoglobin undergoes a conformational change to make it easier for the second and third oxygen molecules to associate- when the haemoglobin molecule starts to become saturated it is harder for the fourth oxygen molecules to bind which is why the graph begins to level off- it is difficult to achieve 100% saturation even at high partial pressures