Numerically integrated growth tracks for three different pebble fluxes or metallicity models (row-to-row) and different Stokes numbers (column-to-column). In the constant St_χ model, St = 0.01, 0.03 and 0.06 are employed to set the initial St at radial distance R₁ (see top panel Fig. 2). Protoplanets with initial mass of M₀ = 0.01 M_⊕ are placed at r₀ = 20, 50 or 80 AU at different formation times (values indicated in the legend). We stop the integration either at the end of the disk lifetime of t_f = 5 Myr or earlier if they reach M_iso, indicated by the gray dashed-dotted line. When Z is constant, which is equivalent to assuming that the pebble-to-gas flux ratio in the inner regions is constant, the growth tracks are independent of t_0,p. Consequently, the growth is overestimated compared to constant St and St_χ, especially when St = 0.03 or 0.06 and when t_0,p = 0.5 Myr or 0.8 Myr. Models with constant St_χ and St from Eqs. (36) and (32), respectively, yield similar results.