Recently, a detailed analysis of the physical properties characterizing a good number of well known dynamical families has been undertaken in order to derive from observational data (proper elements and sizes) some information about the outcomes of catastrophic collisions in the asteroid belt. The advantage of this approach, is that it is based directly on the observed behaviour of real asteroids, and does not require uncertain extrapolations of the results of laboratory experiments involving cm-sized bodies. In particular, new models for the size distribution and the velocity-size relationship of the fragments produced by impacts have been obtained, as a function of impact energy. Coupled with a new, fast technique for the computation of impact probabilities in different zones of the belt, the above results can be implemented in an updated numerical model of the asteroid collisional evolution. Apart from a general application to the evolution of the whole asteroid belt, this model can be applied to an assessment of presently accepted mechanisms of production of NEAs. In particular, we can test whether the production of sizeable NEAs is necessarily accompanied by the formation of some observable dynamical family in the neighbourhood of the main resonances crossing the asteroid belt. Some preliminary results are shown.
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