  The presence of an imposed external magnetic field may drastically influence
the structure of thin accretion discs. The magnetic field energy is here
assumed to be in balance with the thermal energy of the accretion flow. The
vertical magnetic field, its toroidal component B^tor at the disc surface (due
to different rotation rates between disc and its magnetosphere), the turbulent
magnetic Prandtl number and the viscosity-alpha are the key parameters of our
model. Inside the corotation radius for rather small B^tor the resulting
inclination angle i of the magnetic field lines to the disc surface normal can
exceed the critical value 30^\circ (required to launch cold jets) even for
small magnetic Prandtl numbers of order unity. The self-consistent
consideration of both magnetic field and accretion flow demonstrates a weak
dependence of the inclination (``dragging'') angle on the magnetic Prandtl
number for given surface density but a strong dependence on the toroidal field
component at the disc surface.
  A magnetic disc is thicker than a nonmagnetic one for typical parameter
values. The accretion rate can be strongly amplified by large B^tor and small
magnetic Prandtl number. On the other hand, for given accretion rate the
magnetised disc is less massive than the standard-alpha disc. The surface
values of the toroidal magnetic fields which are necessary to induce
considerably high values for the inclination angle are much smaller than
expected and are of order 10^-3 of the imposed vertical field. As the innermost
part of the disc produces the largest B^tor, the largest radial inclination can
be expected also there. The idea is therefore supported that the cold jets are
launched only in the central disc area.
