  Mini-Neptunes seem to be common planets. In this work we investigate the
possible formation histories and predicted occurrence rates of mini-Neptunes
assuming the planets form beyond the iceline. We consider pebble and
planetesimal accretion accounting for envelope enrichment and two different
opacity conditions. We find that the formation of mini-Neptunes is a relatively
frequent output when envelope enrichment by volatiles is included, and that
there is a "sweet spot" for mini-Neptune formation with a relatively low solid
accretion rate of ~10^{-6} Earth masses per year. This rate is typical for
low/intermediate-mass protoplanetary disks and/or disks with low metallicities.
With pebble accretion, envelope enrichment and high opacity favor the formation
of mini-Neptunes, with more efficient formation at large semi-major axes (~30
AU) and low disk viscosity. For planetesimal accretion, such planets can form
also without enrichment, with the opacity being a key aspect in the growth
history and favorable formation location. Finally, we show that the formation
of Neptune-like planets remains a challenge for planet formation theories.
