Cumulative collision rate as a function of the number of GCs, in the case of a homogeneous spherical distribution (left panel), and of a disc distribution (middle and right panels). The colour code refers to the size of the spherical halo (left panel), the radial scale length of the disc (middle panel) for a fixed scale height of 0.8 kpc, and the vertical scale height (right panel) for a fixed scale length of 2 kpc. In each plot, the inset shows a zoom for a number of clusters between 40 and 150. In the inset in the middle and right panels, the asterisk indicates the collision rate corresponding to a disc of scale length of 2 kpc and scale height of 0.8 kpc.