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.
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