  We discuss recent progress in understanding the launching of outflows/jets
from the disc-magnetosphere boundary of slowly and rapidly rotating magnetized
stars. In most of the discussed models the interior of the disc is assumed to
have a turbulent viscosity and magnetic diffusivity (as described by two
``alpha'' parameters), whereas the coronal region outside of the disc is
treated using ideal magnetohydrodynamics (MHD).
  Extensive MHD simulations have established the occurrence of long-lasting
outflows in both the cases of slowly and rapidly rotating stars. In the case of
{\it slowly rotating stars}, a new type of outflow, {\it a conical wind}, is
found and studied in simulations. The conical winds appear in cases where the
magnetic flux of the star is bunched up by the inward motion of the accretion
disc. Near their region of origin, the winds have the shape of a thin conical
shell with a half-opening angle of $ \sim 30^\circ$. At large distances these
outflows become magnetically collimated by their toroidal magnetic field and
form matter dominated jets. That is, the jets are current carrying. The
predominant driving force for the conical winds is the magnetic force
proportional to the negative gradient of the square of the toroidal magnetic
field and not the centrifugal force. In the case of {\it rapidly rotating
stars} in the ``propeller regime,'' a two-component outflow is observed. The
first component is similar to the matter dominated conical winds. A large
fraction of the disc matter may be ejected into the winds in this regime. The
second component is a high-velocity, low-density magnetically dominated {\it
axial jet} where matter flows along the opened polar field lines of the star.
