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We discuss recent progress in understanding the launching of outflows/jetsfrom the disc-magnetosphere boundary of slowly and rapidly rotating magnetizedstars. In most of the discussed models the interior of the disc is assumed tohave a turbulent viscosity and magnetic diffusivity (as described by two``alpha'' parameters), whereas the coronal region outside of the disc istreated using ideal magnetohydrodynamics (MHD).  Extensive MHD simulations have established the occurrence of long-lastingoutflows 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}, isfound and studied in simulations. The conical winds appear in cases where themagnetic flux of the star is bunched up by the inward motion of the accretiondisc. Near their region of origin, the winds have the shape of a thin conicalshell with a half-opening angle of $ \sim 30^\circ$. At large distances theseoutflows become magnetically collimated by their toroidal magnetic field andform matter dominated jets. That is, the jets are current carrying. Thepredominant driving force for the conical winds is the magnetic forceproportional to the negative gradient of the square of the toroidal magneticfield and not the centrifugal force. In the case of {\it rapidly rotatingstars} in the ``propeller regime,'' a two-component outflow is observed. Thefirst component is similar to the matter dominated conical winds. A largefraction of the disc matter may be ejected into the winds in this regime. Thesecond component is a high-velocity, low-density magnetically dominated {\itaxial jet} where matter flows along the opened polar field lines of the star.

Magnetically Driven and Collimated Jets from the Disc-Magnetosphere Boundary of Rotating Stars