A model of the pellet deposition profile is presented, which describes in a self-consistent way the homogenization process and the simultaneous drift of the ablated material. Its main features are (i) that the drift is stopped by a parallel current that appears in the drifting flux tube and reduces the polarization of the expanding ablatant and (ii) that the pellet material does not move as a solid body but homogenizes in a radial interval of extent equal to its displacement. From the pellet and plasma pre-injection characteristics, the model yields the post-injection density and temperature profiles, allowing a quantitative comparison with measurements. The simulation results are compared with experimental data for both the homogenization phase and ∇B-induced displacement. In particular, (i) the calculated characteristics of the homogenization and drift (time constants and velocities) are in agreement with the measurements, (ii) for pellets launched from the low field side (LFS), the model reproduces the dependence of both the fuelling efficiency and the outward displacement on the pellet penetration and (iii) for pellets launched from the high field side (HFS), which are less documented, the calculated fuelling efficiency is always equal to 100%, larger than what is observed, suggesting a transient increase in the plasma (radial) transport. Practically, the main results are that the displacement is smaller for the HFS than for the LFS launched pellets and that, for deep fuelling, one must inject the pellet along the drift direction.