  We construct and analyze a model of the relativistic steady-state
magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric
flow (with one ignorable Cartesian coordinate) propagates under a steep drop of
the external pressure profile. Using the method of self-similarity we derive a
system of ordinary differential equations that describe the flow dynamics. In
the specific limit of an initially homogeneous flow we also provide analytical
results and accurate scaling laws. We consider that limit as a generalization
of the previous Newtonian and hydrodynamic solutions already present in the
literature. The model includes magnetic field and bulk flow speed having all
components, whose role is explored with a parametric study.
