### Abstract:

This paper examines a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the atmosphere of a magnetized and rotating central object with possibly an orbiting accretion disk. The plasma is driven against gravity by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflow starts almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is also given, as well as a brief sketch of its applicability to a self-consistent modelling of collimated outflows from various astrophysical objects. {The analysed model succeeds to give for the first time an exact and self-consistent MHD solution for jet-type outflows extending from the stellar surface to infinity where it can be superfast, in agreement with the MHD causality principle.

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