  The merging history of dark matter halos is computed with the Merging Cell
Model proposed by Rodrigues & Thomas (1996). While originally discussed in the
case of scale-free power spectra, it is developed and tested here in the
framework of the cold dark matter cosmology. The halo mass function, the mass
distribution of progenitors and child halos, as well as the probability
distribution of formation times, have been computed and compared to the
available analytic predictions. The halo auto-correlation function has also
been obtained (a first for a semi-analytic merging tree), and tested against
analytic formulae. An overall good agreement is found between results of the
model, and the predictions derived from the Press & Schechter theory and its
extensions. More severe discrepancies appear when formulae that better describe
N-body simulations are used for comparison. In many instances, the model can be
a useful tool for following the hierarchical growth of structures. In
particular, it is suitable for addressing the issue of the formation and
evolution of galaxy clusters, as well as the population of Lyman-break galaxies
at high redshift, and their clustering properties.
