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 \sim 10 ^ { -6 } M _ { \oplus } /yr .
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 ( \sim 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 .