SIMBAD references

We aim to study the migration of growing dust grains in protoplanetary discs, where growth and migration are tightly coupled. This includes the crucial issue of the radial-drift barrier for growing dust grains. We therefore extend the study performed in Paper I, considering models for grain growth and grain dynamics where both the migration and growth rate depend on the grain size and the location in the disc. The parameter space of disc profiles and growth models is exhaustively explored. In doing so, interpretations for the grain motion found in numerical simulations are also provided. We find that a large number of cases is required to characterize entirely the grains radial motion, providing a large number of possible outcomes. Some of them lead dust particles to be accreted on to the central star and some of them do not. We find then that q < 1 is required for discs to retain their growing particles, where q is the exponent of the radial temperature profile T(R) ∝R^-q. Additionally, the initial dust-to-gas ratio has to exceed a critical value for grains to pile up efficiently, thus avoiding being accreted on to the central star. Discs are also found to retain efficiently small dust grains regenerated by fragmentation. We show how those results are sensitive to the turbulent model considered. Even though some physical processes have been neglected, this study allows us to sketch a scenario in which grains can survive the radial-drift barrier in protoplanetary discs as they grow.