  Using relativistic, steady, axisymmetric, ideal magnetohydrodynamics (MHD) we
analyze the super-Alfvenic regime of a pulsar wind by means of solving the
momentum equation along the flow as well as in the transfield direction.
Employing a self-similar model, we demonstrate that ideal MHD can account for
the full acceleration from high (>>1) to low (<<1) values of $\sigma$, the
Poynting-to-matter energy flux ratio. The solutions also show a transition from
a current-carrying to a return-current regime, partly satisfying the
current-closure condition. We discuss the kind of the boundary conditions near
the base of the ideal MHD regime that are necessary in order to have the
required transition from high to low $\sigma$ in realistic distances, and argue
that this is a likely case for an equatorial wind. Examining the MHD
asymptotics in general, we extend the analysis of Heyvaerts & Norman and
Chiueh, Li, & Begelman by including two new elements: classes of quasi-conical
and parabolic field line shapes that do not preclude an efficient and much
faster than logarithmic acceleration, and the transition $\sigma=\sigma_c$
after which the centrifugal forces (poloidal and azimuthal) are the dominant
terms in the transfield force-balance equation.
