  We consider collision of two geodesic particles moving around rotating
stationary axially symmetric black holes. It is shown for arbitrary
nonequatorial motion that under certain conditions the energy in their centre
of mass frame can grow unbound (the so-called BSW effect). This generalizes the
previous results for equatorial motion around dirty (surrounded by matter)
black holes and nonequatorial motion around the Kerr metric. It turns out that
the BSW effect occurs near any point of the horizon surface. We do not use
special symmetries of space-time typical of the Kerr metric, so the results are
quite generic. The general scheme classifying all possible scenarios is
discussed.
