  We investigate the effect of fragmentation on the homogeneous free cooling of
inelastic hard spheres, using Boltzmann kinetic theory and Direct Monte Carlo
simulations. We analyze in detail a model where dissipative collisions may
subsequently lead to a break-up of the grains. With a given probability, two
off-springs are then created from one of the two colliding partners, with
conservation of mass, momentum and kinetic energy. We observe a scaling regime
characterized by a single collisional average, that quantifies the deviations
from Gaussian behaviour for the joint size and velocity distribution function.
We also discuss the possibility of a catastrophe whereby the number of
particles diverges in a finite time. This phenomenon appears correlated to a
``shattering'' transition marked by a delta singularity at vanishingly small
grains for the rescaled size distribution.
