  We investigate polaron formation in a many-electron system in the presence of
a local repulsion sufficiently strong to prevent local-bipolaron formation.
Specifically, we consider a Hubbard-Holstein model of interacting electrons
coupled to dispersionless phonons of frequency $\omega_0$. Numerically solving
the model in a small one-dimensional cluster, we find that in the nearly
adiabatic case $\omega_0 < t$, the necessary and sufficient condition for the
polaronic regime to occur is that the energy gain in the atomic (i.e.,
extremely localized) regime ${\cal E}_{pol}$ overcomes the energy of the purely
electronic system $ {\cal E}_{el}$. In the antiadiabatic case, $\omega_0 > t$,
polaron formation is instead driven by the condition of a large ionic
displacement $g/\omega_0 >1$ ($g$ being the electron-phonon coupling).
Dynamical properties of the model in the weak and moderately strong coupling
regimes are also analyzed.
