  We present in detail a theoretical model for fragmentation reactions of
three--body halo nuclei. The different reaction mechanisms corresponding to the
different processes are described and discussed. Coulomb and nuclear
interactions are simultaneously included and the method is therefore applicable
for any target, light, intermediate and heavy. Absolute values of many
differential cross sections are then available as function of beam energy and
target. We apply the method to fragmentation of $^6$He and $^{11}$Li on C, Cu
and Pb. A large variety of observables, cross sections and momentum
distributions, are computed. In almost all cases we obtain good agreement with
the available experimental data.
