  It is shown that when only the condition} $0<\Omega_{\rm F}<\Omega_{\rm H}$
is satisfied, the Kerr black hole frame-drags its surrounding force-free
magnetosphere with the field-line-angular-velocity (FLAV) $\Omega_{\rm F}$,
where $\Omega_{\rm H}$ is the horizon angular-velocity. Then, the
zero-angular-momentum-observers (ZAMOs) circulating with the
frame-dragging-angular-velocity $\omega$ will see that the `null surface'
S$_{\rm N}$ where $\omega_{\rm N}=\Omega_{\rm F}$ always exists. They will see
that the outer domain $D_{\rm (out)}$ outside S$_{\rm N}$ is prograde-rotating
with $\Omega_{{\rm F} \omega}>0$, whereas the inner domain $D_{\rm (in)}$
inside is retrograde-rotating with $\Omega_{{\rm F} \omega}<0$, where
$\Omega_{{\rm F} \omega}=\Omega_{{\rm F}} - \omega$ denotes the ZAMO-FLAV.
`This surface' S$_{\rm N}$ must be the magneto-centrifugal divider of the
force-free magnetosphere, with a kind of plasma-shed on it. Subsequently, the
force-free and freezing-in conditions break down on S$_{\rm N}$, thereby
allowing the particle-current sources to be set up on S$_{\rm N}$. `This
surface' also is the ZAM-surface S$_{\rm ZAMD}$, on which no flow of angular
momentum nor electric current can cross. Because the electric field ${\bf
E}_{\rm p}$ reverses sign on S$_{\rm N}$, the Poynting flux reverses direction
from outward to inward on S$_{\rm N}$. An electromagnetic self-extraction of
energy will be possible only through the frame-dragged magnetosphere, with the
inner domain $D_{\rm (in)}$ nested between the horizon and `this surface'
S$_{\rm N}$, in order to comply with the first and second laws of
thermodynamics.
