(a) Growth tracks of protoplanets around a 0.01 M_⊙ brown dwarf (thin) and a 0.1 M_⊙ star (thick). The birth locations of protoplanets are at r = 0.06 AU (red), the water-ice line (orange), and r = 1 AU (blue). The protoplanets are all assumed to form at t = 0 Myr and their masses are adopted from Eq. (14) with γ = 1. In the beginning, disks are dominated by viscous heating, and r_ice = 0.12 AU and 0.55 AU for systems around the 0.01 M_⊙ brown dwarf and 0.1 M_⊙ star, respectively. (b) Time evolution of the water-ice line locations (black) and the semimajor axis of the planet (orange) for systems around stars of different masses. In these two panels the pebble-to-gas mass flux ratio is adopted to be 3%, corresponding to the stellar metallicity [Fe∕H] of 0.48. The inward movement of the ice line is faster in disks around brown dwarfs, while the migration of the protoplanets formed at the ice line is more significant around low-mass M-dwarfs. The water fraction of planets formed at the water-ice line increases with stellar mass.