  We study semi-analytical time-dependent solutions of the relativistic
magnetohydrodynamic (MHD) equations for the fields and the fluid emerging from
a spherical source. We assume uniform expansion of the field and the fluid and
a polytropic relation between the density and the pressure of the fluid. The
expansion velocity is small near the base but approaches the speed of light at
the light sphere where the flux terminates. We find self-consistent solutions
for the density and the magnetic flux. The details of the solution depend on
the ratio of the toroidal and the poloidal magnetic field, the ratio of the
energy carried by the fluid and the electromagnetic field and the maximum
velocity it reaches.
