Density contours of the accretion flow depicted over 5 orders of magnitude in scale separation for run HS at time t = 111,650 r_g/c. The top-left panel shows the full extent of the disk (outer radius ≈5 × 10⁴ r_g = 6400 au). Subsequent zoom-ins follow the gas down to the event horizon (black). We also show the ergosphere (gray shaded pumpkin-shape) for the nearly maximally rotating (a = 0.9375) BH. In each panel we also draw contours of the square root of the axisymmetrized poloidal magnetic flux (Equation (4)), where solid/dashed lines indicate +/- values of Φ_P. The large-scale (≳200 r_g = 26 au) disk contains poloidal flux structures of alternating polarity, whereas closer to the event horizon, the field is dipolar.