  A modified version of the extended Press-Schechter model for the growth of
dark-matter haloes was introduced in two previous papers with the aim at
explaining the mass-density relation shown by haloes in high-resolution
cosmological simulations. In this model major mergers are well separated from
accretion, thereby allowing a natural definition of halo formation and
destruction. This makes it possible to derive analytic expressions for halo
formation and destruction rates, the mass accretion rate, and the probability
distribution functions of halo formation times and progenitor masses. The
stochastic merger histories of haloes can be readily derived and easily
incorporated into semi-analytical models of galaxy formation, thus avoiding the
usual problems encountered in the construction of Monte Carlo merger trees from
the original extended Press-Schechter formalism. Here we show that the
predictions of the modified Press-Schechter model are in good agreement with
the results of N-body simulations for several scale-free cosmologies.
