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.
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