We consider the background of a rotating axially symmetric black hole. Let particle 0 decay to two fragments 1 and 2 in the direction parallel to that of particle 0. It is shown that if decay occurs inside the ergoregion, both particles 1 and 2 move in the same direction as particle 0. For the scenario, when decay happens in the turning point of all three particles, we find the condition when angular momenta of both particles 1 and 2 have the same sign. We elucidate the relation between the approach of Wald that imposes constraint on maximum and minimum energies of fragments and our approach. In doing so, we express the results in terms of characteristics of particle 0 and all particle masses. The conditions of the maximum efficiency depending on the relation between masses is discussed. We find an explicit expression for angular momenta of particles 1 and 2. We discuss also particle decay for static black holes, when the Penrose process is impossible. Because of the absence of the ergoregion in the static case, scenarios of decay for static black holes can significantly differ from those in the rotating background.

34 pages. Presentation improved and expanded, refs. 39, 40 added. Typos in eq. (169) corrected. To appear in PRD