Comparison between t_drift and t_grow in both the sublimation and fragmentation model for a 1.00 M_⊙ star. For both models, t_grow < t_drift in the inner disc, suggesting (runaway) coagulation could occur. However, while the fragmented pebbles remain stuck around the snowline for tens of thousands of years, four orders of magnitude longer than their growth timescale, pebbles in the sublimation model drift into the star in only a few years, giving them significantly less time to grow. It is therefore unlikely that runaway coagulation would be a serious problem in the sublimation model.