  We have used merger trees realizations to study the formation of dark matter
haloes. The construction of merger-trees is based on three different pictures
about the formation of structures in the Universe. These pictures include: the
spherical collapse (SC), the ellipsoidal collapse (EC) and the non-radial
collapse (NR). The reliability of merger-trees has been examined comparing
their predictions related to the distribution of the number of progenitors, as
well as the distribution of formation times, with the predictions of analytical
relations. The comparison yields a very satisfactory agreement. Subsequently,
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