How planets form around different mass stars? In this study, we try to figure out what process sets the final masses of the planets. We developed a pebble-driven core accretion model to study the formation and evolution of planets around stars in the stellar mass range of 0.08 M⊙-1 M⊙. By Monte Carlo sampling of the initial conditions, the growth and migration of a large number of individual protoplanetary embryos were simulated in a population synthesis manner. The forming planets are compared with the observed exoplanets, with respect to planetary mass, semimajor axis, metallicity, and water content. 

We find that gas giant planets are likely to form when the gas disk sizes are larger, the disk accretion rates are higher, the disks are more metal-rich, and/or their stellar hosts are more massive. Our model shows that, first, the characteristic mass of super-Earth is set by the pebble isolation mass. This mass refers to that a planet starts to open a shallow gap and reverses the local pressure gradient. In this circumstance, pebble drift and stop at the local pressure maximum exterior to the planet orbit. Thus, the core mass growth by pebble accretion is halted.  Super-Earth masses increase linearly with the masses of its stellar hosts, which corresponding to one Earth mass around a late M-dwarf star and 20 Earth masses around a solar-mass star. Second, the low-mass planets, up to 20 M⊕, can form around stars with a wide range of metallicities, while massive gas giant planets are preferred to grow around metal-rich stars.  Altogether, our model succeeds in quantitatively reproducing several important observed properties of exoplanets and correlations with their stellar hosts. See details for Liu et al. 2019, A&A  [ADS] [arxiv].