  We calculate the spectral function of the one dimensional Hubbard-Holstein
model using the time dependent Density Matrix Renormalization Group (tDMRG),
focusing on the regime of large local Coulomb repulsion, and away from
electronic half-filling. We argue that, from weak to intermediate
electron-phonon coupling, phonons interact only with the electronic charge, and
not with the spin degrees of freedom. For strong electron-phonon interaction,
spinon and holon bands are not discernible anymore and the system is well
described by a spinless polaronic liquid. In this regime, we observe multiple
peaks in the spectrum with an energy separation corresponding to the energy of
the lattice vibrations (i.e., phonons). We support the numerical results by
introducing a well controlled analytical approach based on Ogata-Shiba's
factorized wave-function, showing that the spectrum can be understood as a
convolution of three contributions, originating from charge, spin, and lattice
sectors. We recognize and interpret these signatures in the spectral properties
and discuss the experimental implications.
