  An axisymmetric MHD model is examined analytically to illustrate some key
aspects of the physics of hot and magnetized outflows which originate in the
near environment of a central gravitating body. By analyzing the asymptotical
behaviour of the outflows it is found that they attain a variety of shapes such
as conical, paraboloidal or cylindrical. However, non cylindrical asymptotics
can be achieved only when the magnetic pinching is negligible and the outflow
is overpressured on its symmetry axis. In cylindrical jet-type asymptotics, the
outflowing plasma reaches an equilibrium wherein it is confined by magnetic
forces or gas pressure gradients, while it is supported by centrifugal forces
or gas pressure gradients. In which of the two regimes (with thermal or
magnetic confinement) a jet can be found depends on the efficiency of the
central magnetic rotator. The radius and terminal speed of the jet are
analytically given in terms of the variation across the poloidal streamlines of
the total energy. Large radius of the jet and efficient acceleration are best
obtained when the external confinement is provided with comparable
contributions by magnetic pinching and thermal pressure. In most cases,
collimated streamlines undergo oscillations with various wavelengths, as also
found by other analytical models. Scenarios for the evolution of outflows into
winds and jets in the different confinement regimes are shortly outlined.
