  We consider axisymmetric stationary dirty black holes with regular
non-extremal or extremal horizons, and compute their on-horizon Petrov types.
The Petrov type (PT) in the frame of the observer crossing the horizon can be
different from that formally obtained in the usual (but singular in the horizon
limit) frame of an observer on a circular orbit. We call this entity the
boosted Petrov type (BPT), as the corresponding frame is obtained by a singular
boost from the regular one. The PT off-horizon can be more general than PT
on-horizon and that can be more general than the BPT on horizon. This is valid
for all regular metrics, irrespective of the extremality of the horizon. We
analyze and classify the possible relations between the three characteristics
and discuss the nature and features of the underlying singular boost. The three
Petrov types can be the same only for space-times of PT D and O off-horizon.
The mutual alignment of principal null directions and the generator in the
vicinity of the horizon is studied in detail. As an example, we also analyze a
special class of metrics with utra-extremal horizons (for which the regularity
conditions look different from the general case) and compare their off-horizon
and on-horizon algebraic structure in both frames.
