We use N -body simulations to study the infall of dark matter haloes onto rich clusters of galaxies .
After identification of all cluster progenitors in the simulations , we select those haloes which accrete directly onto the main cluster progenitor .
We construct the mass function of these merging satellites , and calculate the main orbital parameters for the accreted lumps .
The average circularity of the orbits is \epsilon \simeq 0.5 , while either radial or almost circular orbits are equally avoided .
More massive satellites move along slightly more eccentric orbits , with lower specific angular momentum and a smaller pericentre .
We find that the infall of satellites onto the main cluster progenitor has a very anisotropic distribution .
This anisotropy is to a large extent responsible for the shape and orientation of the final cluster and of its velocity ellipsoid .
At the end of the simulations , the major axis of the cluster is aligned both with that of its velocity ellipsoid , and with the major axis of the ellipsoid defined by the satellite infall pattern , to \approx 30 \degr on average .
We also find that , in lower mass clusters , a higher fraction of the final virial mass is provided by small , dense satellites .
These sink to the centre of the parent cluster and so enhance its central density .
This mechanism is found to be partially responsible for the correlation between halo masses and characteristic overdensities , recently highlighted by Navarro , Frenk & White ( 1996 ) .