Monte Carlo sampling plot of the planet mass as a function of the stellar mass, with the ice-line planet formation model (Scenario A) on the left, the log-uniform distributed planet formation model (Scenario B) on the right, the self-gravitating disks (γ = 1) at the top and the non-self-gravitating disks (γ ≠ 1) at the bottom. The color corresponds to the water mass fraction in the planetary core. The black line stands for a constant planet-to-star mass ratio of 3 × 10⁻⁵ motivated by Pascucci et al. (2018), which also approximates to the pebble isolation mass scaling (Lambrechts et al. 2014; Liu et al. 2019a). There is still an obvious M_p − M_⋆ correlation for the central hosts in the ultra-cool dwarf mass regime of 0.01 M_⊙ and 0.1 M_⊙. This correlation is independent of the birth locations of protoplanets but relies on the disk conditions. Protoplanets can grow to the mass of Mars around 10M_Jup brown dwarfs when they are born in the self-gravitating disk phase, while they only reach 10⁻³ − 10⁻² M_⊕ when the protoplanets form later in the non-self-gravitating disk phase. Planets with ≳ 15% water can form at the water-ice line, while protoplanets formed over a wide range of disk distances end up with a distinctive bimodal water mass.