  Supernovae (SNe) are considered to have a major role in dust enrichment of
high redshift galaxies and, due to the short lifetimes of interstellar grains,
in dust replenishment of local galaxies. Here we explore how SN dust yields
depend on the mass, metallicity, and rotation rate of the progenitor stars, and
on the properties of the explosion. To this aim, assuming uniform mixing inside
the ejecta, we quantify the dust mass produced by a sample of SN models with
progenitor masses $13~M_{\odot} \leq M \leq 120~M_{\odot}$, metallicity $\rm -3
\leq [Fe/H] \leq 0$, rotation rate $\rm v_{\rm rot} = 0$ and $300$~km/s, that
explode with a fixed energy of $1.2 \times 10^{51}$~erg (FE models) or with
explosion properties calibrated to reproduce the $\rm ^{56}Ni$ - $M$ relation
inferred from SN observations (CE models). We find that rotation favours more
efficient dust production, particularly for more massive, low metallicity
stars, but that metallicity and explosion properties have the largest effects
on the dust mass and its composition. In FE models, SNe with $M \leq 20 - 25
~M_{\odot}$ are more efficient at forming dust: between 0.1 and 1 $M_\odot$ is
formed in a single explosion, with a composition dominated by silicates, carbon
and magnetite grains when $\rm [Fe/H] = 0$, and by carbon and magnetite grains
when $\rm [Fe/H] < 0$. In CE models, the ejecta are massive and metal-rich and
dust production is more efficient. The dust mass increases with $M$ and it is
dominated by silicates, at all [Fe/H].

Solar and Stellar Astrophysics;Astrophysics of Galaxies