Electron-phonon coupling, diagonal in a real space formulation, leads to a polaron paradigm of smoothly varying properties. However, fundamental changes, namely the singular behavior of polarons, occur if offdiagonal pairing is involved into consideration. The study of polaron transformations and related properties of matter is of particular interest for realistic models, since competition between diagonal and off-diagonal electron-phonon contributions in the presence of other strong interactions can result in unconventional behavior of the system. Here we consider a two-dimensional multiband pd model of cuprate superconductors with electron-phonon interaction and analyze the features of the systems that are caused by the competition of diagonal and off-diagonal electron-phonon contributions in the limit of strong electron correlations. Using the polaronic version of the generalized tight-binding method, we describe the evolution of the band structure, Fermi surface, density of states at Fermi level, and phonon spectral function in the space of electron-phonon parameters ranging from weak to strong coupling strength of the adiabatic limit. On the phase diagram of polaron properties we reveal two quantum phase transitions and show how electron-phonon interaction gives rise to Fermi surface transformation (i) from hole pockets to true Fermi arcs and (ii) from hole to electron type of conductivity. We also demonstrate the emergence of new states in the phonon spectral function of the polaron and discuss their origin.

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