Splitting of the Alfven surface in a relativistic pulsar wind

In a recent paper, Li and Melrose have claimed that the splitting - due to relativistic effects - of the Alfven surface in an axisymmetric pulsar wind does not occur. Here we refute this claim by showing that, unless the solution that describes the flow along each open magnetic field line passes through the pure Alfvenic point (which is one of the manifestations of the splitting of the Alfvenic point), it would not be physically viable both at the surface of the star and at infinity.