  We study the ability of PINOCCHIO (PINpointing Orbit-Crossing Collapsed
HIerarchical Objects) to predict the merging histories of dark matter (DM)
haloes, comparing the PINOCCHIO predictions with the results of two large
N-body simulations run from the same set of initial conditions. We focus our
attention on quantities most relevant to galaxy formation and large-scale
structure studies. PINOCCHIO is able to predict the statistics of merger trees
with a typical accuracy of 20 per cent. Its validity extends to higher-order
moments of the distribution of progenitors. The agreement is valid also at the
object-by-object level, with 70-90 per cent of the progenitors cleanly
recognised when the parent halo is cleanly recognised itself. Predictions are
presented also for quantities that are usually not reproduced by semi-analytic
codes, such as the two-point correlation function of the progenitors of massive
haloes and the distribution of initial orbital parameters of merging haloes.
For the accuracy of the prediction and for the facility with which merger
histories are produced, PINOCCHIO provides a means to generate catalogues of DM
haloes which is extremely competitive to large-scale N-body simulations, making
it a suitable tool for galaxy formation and large-scale structure studies.
