Evolution of the BH–halo centre distance for simulations with the same mass resolution as B1e6_DF_ϵ_∗ but using reduced gravitational softening lengths: ϵ_DM = 0.72, ϵ_BH = ϵ_∗ = 0.25. The green curves show the results from these simulations, with the darker line corresponding to the run without dynamical friction (NODF_LOWSOFT) and the lighter green line including the DF correction (DF_LOWSOFT). For reference, we plot in yellow and purple the outcome of B1e6_DF_ϵ_∗ and B1e6_NODF_ϵ_∗, while blue curves shows the results from B1e6_NODF_ϵ_DM (light) and B1e6_DF_ϵ_DM (dark). The red line represents the analytical predictions from OTIS.