It is commonly accepted that the formation of asteroid families is the consequence of catastrophic impacts on former {\em parent bodies} (Hirayama, 1933). But to reproduce the puzzling steep size distributions of the presently known asteroid families has been up to now a task in which recent modelling techniques of fragmentation have typically failed. The role of geometric constraints in the production of fragments in asteroidal collisions is an issue that has been investigated in recent times only by Tanga \al, 1999, and that might give some insight into the understanding of high--velocity collisional processes. Improvements to the approach by Tanga \al are introduced in the present work, in order to take into account in a more realistic way the different shapes that largest remnants may have when formed in high--velocity collisional events involving spherical parent bodies. We also consider the case in which the parent body and the largest remnant are cubes and the fragments are {\it a)} cubes, {\it b)} parallelepipeds, instead of spheres. A somewhat uniform power--law behaviour in the size distributions of the randomly--generated fragments is found in the numerical simulations---not detected by Tanga \al---and an analytical derivation of the upper limit to the corresponding exponent is given. Further improvements are introduced in the model in order to refine it and to allow any fragment to develop any shape, and to account for the fact that fragments form more or less at the same time, not sequentially. Finally, the results of the refined model are compared with the size distributions of the observed actual main belt asteroid families, and encouraging agreement is obtained in most cases.