The application to several triatomic reactions of a novel implementation of absorbing potentials on a generalized R-matrix propagation method [Chem. Phys. Lett. 291, 346 (1998) and J. Chem. Phys. 109, 5761 (1998)] is presented. Specific systems chosen have been Li+FH, Mg+FH and H+F-2, so that an extensive application covering a wide range of potential energy surfaces (PESs) has been performed: it includes moderately and largely exoergic and endoergic processes, simple and involved PES, moderate to large skew angles, and direct and complex-forming collisions. In all cases, it is shown that the use of the absorbing potential is simple and robust, yielding correct values at a fraction of the computer's resources consumption. The best effectiveness is obtained for exothermic, direct reactions, for which up to one order of magnitude in CPU time saving is obtained. This efficiency opened the possibility for a very detailed exploration of the reactive process, in particular on those quantities strongly dependent on the collision energy. In addition, it is shown that, as previously known from a totally different numerical approach, the cumulative reaction probability can be efficiently and accurately calculated propagating the scattering solution along a very short range of the scattering coordinate.