Gas accretion pathway depending on the initial position and formation time of a protoplanet of 0.01 M_⊕ in disks with different pebble Stokes numbers. We employ a disk lifetime of t_f = 5 Myr, an initial metallicity of Z₀ = 0.01 and a midplane turbulence of a_t = 10⁻⁴. The rest of the parameter values are listed in Table 1. Left: protoplanets cannot accrete gas via the pebble decay pathway when the pebbles are small and do not drift significantly. Center: under limited initial conditions, some gas giants form via the pebble decay pathway due to the short-lasting flux for a slightly higher value of St. Right: for even higher values of St the decay of the flux occurs earlier, and therefore, protoplanets must emerge at even earlier stages to reach M_iso. The pebble decay pathway is less pronounced in this case.