  Context. To form metre-sized pre-planetesimals in protoplanetary discs,
growing grains have to decouple from the gas before they are accreted onto the
central star during their phase of fast radial migration and thus overcome the
so-called "radial-drift barrier" (often inaccurately referred to as the
"metre-size barrier"). Aims. To predict the outcome of the radial motion of
dust grains in protoplanetary discs whose surface density and temperature
follow power-law profiles, with exponent p and q respectively. We investigate
both the Epstein and the Stokes drag regimes which govern the motion of the
dust. Methods. We analytically integrate the equations of motion obtained from
perturbation analysis. We compare these results with those from direct
numerical integration of the equations of motion. Then, using data from
observed discs, we predict the fate of dust grains in real discs. Results. When
a dust grain reaches the inner regions of the disc, the acceleration due to the
increase of the pressure gradient is counterbalanced by the increase of the gas
drag. We find that most grains in the Epstein (resp. the Stokes) regime survive
their radial migration if-p+q+1/2 \leq0 (resp. if q\leq 2/3). The majority of
observed discs satisfies both-p+q+ 1/2 \leq0 and q\leq 2/3: a large fraction of
both their small and large grains remain in the disc, for them the radial drift
barrier does not exist.
