Sketch of the possible phases an enriched protoplanet could follow after reaching the critical mass. Although not illustrated (for not overloading the image), planetesimal accretion is present in all the stages and the material assumed to remain in the envelope. Despite the competition between gas and planetesimal accretion, the immediate result would be dilution, since at this point the accretion of gas is larger than that of solids, as explained in the main text. As a consequence of dilution, M_crit increases. After this point, depending on the accretion rate of planetesimals (which gives a new M_Z) versus the accretion rate of gas from the disc, the planet could become sub-critical or super-critical, as is discussed in Sect. 6.5.