Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a disk around a compact object, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. Focusing on the parameter regime appropriate to γ-ray burst outflows, we demonstrate, through exact self-similar solutions, that the thermal force (which dominates the initial acceleration) and the Lorentz force (which dominates farther out and contributes most of the acceleration) can convert up to ~50% of the initial total energy into asymptotic baryon kinetic energy. We examine how baryon loading and magnetic collimation affect the structure of the flow, including the regime where emission due to internal shocks could take place.

The modelling of plasma outflows from central gravitating objects such as AGN is briefly discussed via analytic examples in the context of ideal MHD. The exact solutions are produced via a nonlinear separation of the variables in the full set of the MHD equations. Attention is given to the questions of initial acceleration and collimation of the outflow. A quantitative criterion is provided for the transition of the morphologies from highly collimated jets to non collimated winds.