  We show that energy should be dissipated or extracted in the current sheet
(CS) of a split magnetosphere deviating from the Michel split monopole, with
the CS heating up or cooling down. But the electromagnetic energy remains
unchanged everywhere. Based on the de-centered monopole solution generated by
symmetry, we construct two generalized split monopole configurations, in which
the field lines intersect with the CS at arbitrary angles. One configuration
resembles the outer geometry of the so-called ``new pulsar magnetosphere
model", for which up to $47\%$ of the spin down energy is transferred to the
Joule heating process in the CS. The other configuration resembles a split
monopole in the presence of a thin accretion disk that contains magnetic fields
itself. Energy is extracted simultaneously from the central star and the CS to
power the output Poynting flux at infinity. Thus, the spin down energy
extracted from the star can be greatly reduced, even to $11.6\%$ of that by the
Michel split monopole.
