  Previous work concerning planet formation around low-mass stars has often
been limited to large planets and individual systems. As current surveys
routinely detect planets down to terrestrial size in these systems, a more
holistic approach that reflects their diverse architectures is timely. Here, we
investigate planet formation around low-mass stars and identify differences in
the statistical distribution of planets. We compare the synthetic planet
populations to observed exoplanets. We used the Generation III Bern model of
planet formation and evolution to calculate synthetic populations varying the
central star from solar-like stars to ultra-late M dwarfs. This model includes
planetary migration, N-body interactions between embryos, accretion of
planetesimals and gas, and long-term contraction and loss of the gaseous
atmospheres. We find that temperate, Earth-sized planets are most frequent
around early M dwarfs and more rare for solar-type stars and late M dwarfs. The
planetary mass distribution does not linearly scale with the disk mass. The
reason is the emergence of giant planets for M*>0.5 Msol, which leads to the
ejection of smaller planets. For M*>0.3 Msol there is sufficient mass in the
majority of systems to form Earth-like planets, leading to a similar amount of
Exo-Earths going from M to G dwarfs. In contrast, the number of super-Earths
and larger planets increases monotonically with stellar mass. We further
identify a regime of disk parameters that reproduces observed M-dwarf systems
such as TRAPPIST-1. However, giant planets around late M dwarfs such as GJ
3512b only form when type I migration is substantially reduced. We quantify the
stellar mass dependence of multi-planet systems using global simulations of
planet formation and evolution. The results compare well to current
observational data and predicts trends that can be tested with future
observations.
