Snapshots at t = 0   yr and t = 10⁶   yr of dynamical disc evolution showing the mean charge  ⟨ Z ⟩  associated with two different dust topologies as a function of the orbital radius R. The profiles shown in the left panel refer to BCCA agglomerates with N = 10⁶ (top) and N = 10² (bottom) monomers of a₀ = 10^-5   cm. The results obtained for the corresponding compact spheres are shown in the right panel. Here, the radius a_∗ of the compact sphere varies from a_∗ = 10^-3  cm (top) to a_∗ = 4.64 × 10^-5   cm (bottom). The dashed lines are associated with the profiles evaluated after t = 10⁶   yr disc evolution; to aid comparison with the initial profiles we superimposed the corresponding profiles of Fig. 7 using dotted lines. As we did in the preceding figures, we mark the semi-analytical solution with (blue) filled circles.