Sketch of the four evolutionary phases of polluted envelopes (excluding photo-evaporation). During the first phase of direct core growth, a portion of the high-Z material makes it through to the core. This contrasts with the second phase, where only the envelope (M_env = M_xy + M_z − M_c) gains additional mass and all accreted solids are absorbed as vapor (M_z − M_c). Phase II could terminate when the planet enters runaway accretion. Otherwise, if the solids mass flux dries up while the disk is still present, the planet enters a Kelvin–Helmholtz contraction phase (III). This leads to further gas accretion and to the dilution of the envelope. When the disk ultimately dissipates, there is no gas left to accrete and the envelope contracts (IV). This eventually leads to the (partial) sedimentation of high-Z vapor and to the indirect growth of the core.