  We study the small-polaron problem of a single electron interacting with the
lattice for the Holstein model in the adiabatic limit on a comb lattice, when
the electron-phonon interaction acts only on the base sites. The ground state
properties can be easily deduced from the ones of a linear chain with an
appropriate rescaling of the coupling constant. On the other hand, the
dynamical properties, that involve the complete spectrum of the system, present
an "exotic" behavior. In the weak coupling limit the Drude weight
(zero-frequency conductivity) is enhanced with respect to its free-case value,
contrary to the linear chain case, where for every finite value one has a
suppression of the Drude peak. More interestingly, the loss of coherent
electron motion and the polaronic localization of the carrier occurs for
different coupling values. Thus for intermediate coupling, a novel phase
appears with large kinetic energy and no coherent motion.
