  The presence of dust strongly affects the way we see galaxies and also the
chemical abundances we measure in gas. It is therefore important to study he
chemical evolution of galaxies by taking into account dust evolution. We aim at
performing a detailed study of abundance ratios of high redshift objects and
their dust properties. We focus on Lyman-Break galaxies (LBGs) and Quasar (QSO)
hosts and likely progenitors of low- and high-mass present-day elliptical
galaxies, respectively. We have adopted a chemical evolution model for
elliptical galaxies taking account the dust production from low and
intermediate mass stars, supernovae Ia, supernovae II, QSOs and both dust
destruction and accretion processes. By means of such a model we have followed
the chemical evolution of ellipticals of different baryonic masses. Our model
complies with chemical downsizing. We made predictions for the abundance ratios
versus metallicity trends for models of differing masses that can be used to
constrain the star formation rate, initial mass function and dust mass in
observed galaxies. We predict the existence of a high redshift dust
mass-stellar mass relationship. We have found a good agreement with the
properties of LBGs if we assume that they formed at redshift z=2-4. In
particular, a non-negligible amount of dust is needed to explain the observed
abundance pattern. We studied the QSO SDSS J114816, one of the most distant QSO
ever observed (z=6.4), and we have been able to reproduce the amount of dust
measured in this object. The dust is clearly due to the production from
supernovae and the most massive AGB stars as well as from the grain growth in
the interstellar medium. The QSO dust is likely to dominate only in the very
central regions of the galaxies and during the early development of the
galactic wind.
