Sketches of the axisymmetric 2.5D BH magnetosphere for a spin a = 0.99. Top: the black disk (resp. black dashed line) in the bottom left corner is the event horizon of size r_h ∼ 1.14r_g (resp. the ergosphere). The black lines represent open magnetic field lines. The absorbing layer for outer boundary conditions is shown in gray. The red circle locates the Y-point at the basis of the reconnecting current sheet in which plasmoids are visible in red. The green region is the Keplerian disk where magnetic field lines are anchored. Bottom: zoom in on the innermost region, with closed magnetic field lines coupling the disk to the BH represented in red, along with the outermost closed magnetic field line (the separatrix).