The stationary hydrodynamic equations for transonic viscous accretion discs in Kerr geometry are derived. The consistent formulation is given for the viscous angular momentum transport and the boundary conditions on the horizon of a central black hole. An expression for the thickness of the disc is obtained from the vertical Euler equation for general accretion flows with vanishing vertical velocity. Different solution topologies are identified, characterized by a sonic transition close to or far from the marginally stable orbit. A numerical method is presented that allows to integrate the structure equations of transonic accretion flows. Global polytropic solutions for the disc structure are calculated, covering each topology and a wide range of physical conditions. These solutions generally possess a sub-Keplerian angular momentum distribution and have maximum temperatures in the range 10 11 − 10 12 K. Accretion discs around rotating black holes are hotter and deposit less angular momentum on the central object than accretion discs around Schwarzschild black holes.

We investigate the interaction of a protostellar magnetosphere with a large‐scale magnetic field threading the surrounding accretion disc. It is assumed that a stellar dynamo generates a dipolar‐type field with its magnetic moment aligned with the disc magnetic field. This leads to a magnetic neutral line at the disc mid‐plane and gives rise to magnetic reconnection, converting closed protostellar magnetic flux into open field lines. These are simultaneously loaded with disc material, which is then ejected in a powerful wind. This process efficiently brakes down the protostar to 10–20 per cent of the break‐up velocity during the embedded phase.

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An analytic model for a stationary force-free relativistic magnetized jet is presented. In those models a poloidal current provides the tension that balances the internal pressure. Our ignorance of the detailed conditions in the collimation zone is accounted for by specifying the current distribution as an (essentially free) function of the flux surfaces. The asymptotically cylindrical Grad-Schlüter-Shafranov (GSS) equation is solved for a nonlinear current distribution, I(Ψ) = c(1 – exp(−bΨ)) which covers both diffuse (b 《 1) and sharp (b 》 1) pinches, and weak (small c) and strong (large c) currents.

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