Acceleration of particles by quasiblack holes

If two particles collide near the black hole horizon, the energy in the centre of mass (CM) frame can grow indefinitely (the so-called the BSW effect). This requires fine-tuning the parameters (the energy, angular momentum or electric charge) of one particle. We show that the CM energy can be unbound also for collisions in the space-time of quasiblack holes - QBHs (the objects on the threshold of forming the horizon which do not collapse). It does not require special fine-tuning of parameters and occurs when any particle inside a QBH having a finite energy collides with the particle that entered a QBH from the outside region.