Simulated monopolar magnetosphere using the hybrid force-free-PIC scheme. The division between the force-free and PIC domains is the equatorial plane (dashed magenta line in the top and middle panels). Top: Spatial distribution of the radial current density normalized to the fiducial current density, $J_{\mathrm{GJ}}^{\star }$, and compensated by (r/r_⋆)² for visualization purposes, for the 4096² cells run. Solid lines show the poloidal magnetic field lines. Middle: Cross-section of the current density profile at r = 1.5R_LC as a function of the numerical resolution, and comparison with the exact profile (red dashed-dotted line, Eq. 34). Bottom: Radial profiles of the Poynting flux, L(r), normalized to the monopole solution, L_M (Eq. 35), for all three resolutions. Percentages correspond to the amount of numerical dissipation for each run, computed between the flux averaged in the gray areas.