  Observations of relativistic jets from black holes systems suggest that
particle acceleration often occurs at fixed locations within the flow. These
sites could be associated with critical points that allow the formation of
standing shock regions, such as the magnetosonic modified fast point. Using the
self-similar formulation of special relativistic magnetohydrodynamics by
Vlahakis & K\"onigl, we derive a new class of flow solutions that are both
relativistic and cross the modified fast point at a finite height. Our
solutions span a range of Lorentz factors up to at least 10, appropriate for
most jets in X-ray binaries and active galactic nuclei, and a range in injected
particle internal energy. A broad range of solutions exists, which will allow
the eventual matching of these scale-free models to physical boundary
conditions in the analysis of observed sources.
