Relativistic MHD Jets and Their Interactions with the Intra-cluster Medium

We present the formulation of relativistic MHD flows, likely occurring in the environment of accretion onto supermassive black holes. Three-dimensional relativistic MHD simulations will be presented on how the energy outflow will partition among different physical components and on the collimation and stability of such systems. The interaction between such flows with their environment, e.g., the intra-cluster medium, will be discussed.