  We consider collision of two geodesic particles near the horizon of such an
axially symmetric black hole (rotating or static) that the metric coefficient
$g_{\phi \phi }\rightarrow 0$ there. It is shown that (both for regular and
singular horizons) the energy in the centre of mass frame $% E_{c.m.}$ is
indefinitely large even without fine-tuning of particles' parameters.
Kinematically, this is collision between two rapid particles that approach the
horizon almost with the speed of light but at different angles. The latter is
the reason why the relative velocity tends to that of light, hence to high
$E_{c.m.}$. Our approach is model-independent. It relies on general properties
of geometry and is insensitive to the details of material source that supports
the geometies of the type under consideration. For several particular models
(the stringy black hole, the Brans-Dicke analogue of the Schwarzschild metric
and the Janis-Newman-Winicour one) we recover the results found in literature
previously.
