  We consider the behavior of the innermost stable circular orbit (ISCO) in the
magnetic field near "dirty" (surrounded by matter) axially-symmetric black
holes. The cases of near-extremal, extremal and nonextremal black holes are
analyzed. For nonrotating black holes, in the strong magnetic field ISCO
approaches the horizon (when backreaction of the field on geometry is
neglected). Rotation destroys this phenomenon. The angular momentum and radius
of ISCO look model-independent in the main approximation. We also study the
collisions between two particles that results in the ultra-high energy
$E_{c.m.}$ in the centre of mass frame. Two scenarios are considered - when one
particle moves on the near-horizon ISCO or when collision occurs on the
horizon, one particle having the energy and angular momentum typical of ISCO.
If the magnetic field is strong enough and a black hole is slow rotating,
$E_{c.m.}$ can become arbitrarily large. Kinematics of high-energy collision is
discussed. As an example, we consider the magnetized Schwarzschild black hole
for an arbitrary strength of the field (the Ernst solution). It is shown that
backreaction of the magnetic field on the geometry can bound the growth of
$E_{c.m.}$.
