We find that the outcome of the dust migration process is very sensitive to the physical conditions within the disc. For high dust-to-gas ratios (greater than or similar to 0.01) and/or flattened disc structures (H/R less than or similar to 0.05), growing dust grains can efficiently decouple from the gas, leading to a high concentration of grains at a critical radius of a few AU. Decoupling of grains from gas can occur at a large fraction (>0.1) of the initial radius of the particle, for a dust-to-gas ratio greater than approximate to 0.05. Dust grains that experience migration without significant growth (millimetre and centimetre-sized) are efficiently accreted for discs with flat surface density profiles (p < 0.7) while they always remain in the disc if the surface density is steep enough (p > 1.2). Between (0.7 < p < 1.2), both behaviours may occur depending on the exact density and temperature structures of the disc. Both the presence of large grains and vertical settling tend to favour the accretion of non-growing dust grains onto the central object, but it slows down the migration of growing dust grains. If the disc has evolved into a self-shadowed structure, the required dust-to-gas ratio for dust grains to stop their migration at large radius become much smaller, of the order of 0.01. All the disc configurations are found to have favourable temperature profiles over most of the disc to retain their planetesimals.