Previous theoretical works concerning planet formation around low-mass stars were often addressing large planets or individual systems. However, present-day surveys are discovering many planets down to Earth-size around low-mass stars. A picture of very different kinds of planetary systems around low-mass stars currently emerges. We investigate and compare the planetary population for these different conditions. The goal is to understand planet formation around stars with lower stellar masses and identify differences in the statistical distribution of modeled planets.We use the Generation III Bern model of global planet formation and evolution to calculate synthetic populations of up to 50 planets per modeled system 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. A linear scaling of the protoplanetary disk mass with stellar mass is assumed. The resulting synthetic planetary populations for a 0.1 Msol and a solar-type star can be seen in the attached figure. Statistical analysis reveals that temperate, Earth-sized planets are most frequent around early M dwarfs (0.5 Msol) and more rare for both solar-type stars and late M dwarfs. Additionally, we identify a regime of disk parameters that reproduces observed M-dwarf systems such as TRAPPIST-1. However, giant planets around late M dwarfs like GJ 3512b only form when type I migration is substantially inhibited. Furthermore, the planetary mass distribution does not linearly scale with the disk mass. The cause lies in the growth of gaseous, giant planets, which leads to ejection of planets - reducing the apparent efficiency of solid accretion for higher stellar masses. However, this effect is not strong enough to explain the reported higher occurrence rates of planets around M dwarfs. This points towards an additional cause for this trend, which most likely lies in the assembly of planetesimals or in the initial disk conditions.