BH distance from the halo centre over time, starting from an initial position at 20 kpc, with orbital eccentricities e = 0.3, 0.5, 0.8 shown in the first, second, and third columns, respectively. Each row represents a different halo resolution: N_part = 10⁵, 10⁶, 10⁷, 5 · 10⁷ from top to bottom. Yellow lines show results for simulations with P03 softening lengths, and red lines indicate Z19 softenings. Analytical predictions for each orbital eccentricity are represented as a blue line. Dotted lines mark softening values for each resolution (yellow edge for P03, red edge for Z19). All simulations apply the DF correction from D24.