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 1 1 Li on C, Cu and Pb. A<space>large variety of observables, cross sections and momentum distributions, are computed. In almost all cases we obtain good agreement with the available experimental data.