  We take advantage of an analytic model of galaxy formation coupled to the
merger tree of an N-body simulation to study the roles of environment and
stellar mass in the quenching of galaxies. The model has been originally set in
order to provide the observed evolution of the stellar mass function as well as
reasonable predictions of the star formation rate-stellar mass relation, from
high redshift to the present time. We analyse the stellar mass and
environmental quenching efficiencies and their dependence on stellar mass, halo
mass (taken as a proxy for the environment) and redshift. Our analysis shows
that the two quenching efficiencies are redshift, stellar and halo mass
dependent, and that the halo mass is also a good proxy for the environment. The
environmental quenching increases with decreasing redshift and is inefficient
below $\log M_* \sim 9.5$, reaches the maximum value at $\log M_* \sim 10.5$,
and decreases again, becoming poorly efficient at very high stellar mass ($\log
M_* \gtrsim 11.5$). Central and satellites galaxies are mass quenched
differently: for the former, the quenching efficiency depends very weakly on
redshift, but strongly on stellar mass; for the latter, it strongly depends on
both stellar mass and redshift in the range $10\lesssim \log M_* \lesssim 11$.
According to the most recent observational results, we find that the two
quenching efficiencies are not separable: intermediate mass galaxies are
environmental quenched faster, as well as intermediate/massive galaxies in more
massive haloes. At stellar masses lower than $\log M_* \lesssim 9.5$ both
quenching mechanisms become inefficient, independently of the redshift.
