  Numerical simulations of Blandford-Znajek energy extraction at high spin have
revealed that field lines tend to bunch near the poles of the event horizon. We
show that this behavior can be derived analytically from the assumption of
fixed functional dependence of current and field line rotation on magnetic
flux. The argument relies crucially on the existence of the Znajek condition,
which offers non-trivial information about the fields on the horizon without
requiring a full force-free solution. We also provide some new analytic
expressions for the parabolic field configuration.
