  The evolution equations of anomalous magnetohydrodynamics are derived in the
extreme relativistic regime and contrasted with the treatment of hydromagnetic
nonlinearities pioneered by Lichnerowicz in the absence of anomalous currents.
In particular we explore the situation where the conventional vector currents
are complemented by the axial-vector currents arising either from the pseudo
Nambu-Goldstone bosons of a spontaneously broken symmetry or because of finite
fermionic density effects. After expanding the generally covariant equations in
inverse powers of the conductivity, the relativistic analog of the magnetic
diffusivity equation is derived in the presence of vortical and magnetic
currents. While the anomalous contributions are generally suppressed by the
diffusivity, they are shown to disappear in the perfectly conducting limit.
When the flow is irrotational, boost-invariant and with vanishing
four-acceleration the corresponding evolution equations are explicitly
integrated so that the various physical regimes can be directly verified.
