  We study the collimation of relativistic magnetohydrodynamic jets by the
pressure of an ambient medium, in the limit where the jet interior loses causal
contact with its surroundings. This follows up a hydrodynamic study in a
previous paper, adding the effects of a toroidal magnetic field threading the
jet. As the ultrarelativistic jet encounters an ambient medium with a pressure
profile with a radial scaling of p ~ r^-eta where 2<eta<4, it loses causal
contact with its surroundings and forms a boundary layer with a large pressure
gradient. By constructing self-similar solutions to the fluid equations within
this boundary layer, we examine the structure of this layer as a function of
the external pressure profile. We show that the boundary layer always becomes
magnetically dominated far from the source, and that in the magnetic limit,
physical self-similar solutions are admitted in which the total pressure within
the layer decreases linearly with distance from the contact discontinuity
inward. These solutions suggest a `hollow cone' behavior of the jet, with the
boundary layer thickness prescribed by the value of eta. In contrast to the
hydrodynamical case, however, the boundary layer contains an asymptotically
vanishing fraction of the jet energy flux.
