Fragmentation of various fullerenes was studied by surface impact on highly oriented pyrolytic graphite at collision energies E(col) of 150-1050 eV/molecule. The projectiles C-60(+), C-70(+), C-76(+), C-84(+), and C-94(+) were formed by laser desorption of chromatographically separated samples, while large carbon clusters C-94(+), C-110(+), C-164(+) were produced by laser-induced coalescence reactions. Except at the highest impact energies; the fragment distributions consist of even numbered C-n(+) species with abundance maxima similar to those observed in fullerene synthesis. With increasing E(col), we observe a size evolution in the fragment distributions characteristic of a sequential fragmentation process. Simulated fragment distributions based on statistical rate theory and a sequential C-2 loss mechanism reproduce the experimental data well up to a maximum E(col). They are used to determine the mean energy transfer during surface impact as a function of collision energy as well as its dependence on several experimental parameters such as the nature (cleanliness) of the target surface, the internal energy of the incident ion, and the incident fullerene size. Both internal and kinetic energy of the incident ion are found to contribute to the observed fragmentation although with different efficiencies. For the higher fullerenes we find a tendency towards increasing transfer efficiency of incident kinetic to internal energy with increasing projectile size. Finally, above a size-dependent impact energy threshold, a transition to a different high energy fragmentation process is indicated by changes in the fragment distributions. These go from exclusively even numbered fullerene fragments at low impact energy to smaller even and odd numbered C-n(+) fragments at high E(col). It is suggested that this change indicates the formation of high energy, nonfullerene isomers.