Final masses of SMSs at zero metallicity, accreting at the rates of atomically cooled halos. The results of the present work are shown by a solid black line. The masses obtained with the polytropic criterion are shown as dashed lines when applied in the whole star (lower line) and in the convective core only (upper line). The results of Umeda et al. (2016) and Woods et al. (2017), obtained with numerical hydrodynamics, are shown in grey.