A short-range electron-phonon interaction is considered in a strongly correlated many-electron system. The nature of the polarons is investigated as a function of hole concentration for different electron-phonon coupling strengths, through a modified Lang-Firsov transformation where the lattice distortion, produced at different sites around a charge carrier, may be treated as a variational parameter. For a suitable electron-phonon coupling strength small polarons are obtained for both low and high hole concentrations and large polarons become stable in the intermediate hole concentration region. The variation of the polaronic hopping and the intersite polaronic interactions with the hole concentration are presented. The implications of the results in the content of high- T c oxide superconductors are discussed.