  We present a derivation of the entropy of black holes in induced gravity
models based on conformal properties of induced gravity constituents near the
horizon. The four-dimensional (4D) theory is first reduced to a tower of
two-dimensional (2D) gravities such that each 2D theory is induced by fields
with certain momentum $p$ along the horizon. We demonstrate that in the
vicinity of the horizon constituents of the 2D induced gravities are described
by conformal field theories (CFT) with specific central charges depending on
spin and non-minimal couplings and with specific correlation lengths depending
on the masses of fields and on the momentum $p$. This enables one to use CFT
methods to count partial entropies $s(p)$ in each 2D sector. The sum of partial
entropies correctly reproduces the Bekenstein-Hawking entropy of the 4D induced
gravity theory. Our results indicate that earlier attempts of the derivation of
the entropy of black holes based on a near-horizon CFT may have a microscopic
realization.
