A classical two temperature magnetohydrodynamic modelling approach is used to study the influence of a large contact gap (up to 40 mm) on the behaviour of a diffuse vacuum arc controlled by a 5 mT/kA uniform external axial magnetic field between two copper electrodes with a 20 mm radius. The current constriction and energy flux density at the anode surface are more particularly analyzed, considering both supersonic and subsonic flow conditions. In the case of a supersonic arc, simulations show that the constriction of the current develops in the whole interelectrode region, but the constriction level at the anode surface does not evolve monotonically with the contact gap. The constriction is partly correlated to the radial compression of the plasma. In the case of a subsonic arc, the current constriction is related to the presence of the anode sheath. It occurs only close to the anode (from a constant distance from the anode of around 15 mm). Whereas the current constriction at the anode surface increases when the gap length goes from 10 mm to 20 mm, it no longer evolves when increasing the gap length from 20 mm to 40 mm. For both flow conditions, the evolution with the gap length of the radial profile of the energy flux density transferred by the plasma to the anode is similar as that followed by the current constriction at the anode.