Schematic illustration of the sublimation of drifting icy pebbles. In the case of the advection-dominated regime (left; Sect. 3.1), gas accretion onto the central star dominates the radial transport of vapor. The loss of vapor due to the inward advection of the vapor then balances the vapor supply from sublimating icy pebbles. Thus, drifting pebbles sublimate outside the snow line (i.e., r > r_snow). In the case of the diffusion-dominated regime (right; Sect. 3.2), water vapor produced inside the snow line efficiently diffuses outside the snow line, leading to a super-saturation state (P_vap (r) > P_sat(r)). The sublimation of pebbles can therefore take place only inside the snow line (i.e., r < r_snow).