Jets can contribute to the spectra of X-ray binaries (XRBs) and active galactic nuclei (AGN) from the radio through the γ-ray bands; thus understanding their physics is key for interpreting the data. Recent VLBI observations suggest that jets begin to accelerate particles into power-law distributions at a point offset from the black hole by ~104rg, possibly via a collimation shock. Spectral fitting of simultaneous, broadband data from both XRBs and AGN in jet-dominated states corroborates this picture. From a magnetohydrodynamical (MHD) point of view, it is natural to associate the onset of particle acceleration with the final MHD critical point in the flow, the modified fast point (MFP), where causal contact with the upstream flow is broken. In this way a standing disruption like a shock can form, and this location might vary with the physical parameters of the jet. In order to study this issue, we have used the self-similar formalism of Vlahakis & Königl (2003, hereafter VK03) to simplify the MHD equations and to derive solutions that cross the critical points. We have found a new parameter space of solutions that cross the MFP at a finite height above the disc and are relativistic, spanning a range of Lorentz factors Γ ≤ 10 (Polko et al. 2010). We present these results, as well as preliminary work connecting the relativistic formalism to the non-relativistic conditions with gravity near the base of the jets.