  We investigate outflows from the disk-magnetosphere boundary of rotating
magnetized stars in cases where the magnetic field of a star is bunched into an
X-type configuration using axisymmetric and full 3D MHD simulations. Such
configuration appears if viscosity in the disk is larger than diffusivity, or
if the accretion rate in the disk is enhanced. Conical outflows flow from the
inner edge of the disk to a narrow shell with an opening angle 30-45 degrees.
Outflows carry 0.1-0.3 of the disk mass and part of the disk's angular momentum
outward. Conical outflows appear around stars of different periods, however in
case of stars in the "propeller" regime, an additional - much faster component
appears: an axial jet, where matter is accelerated up to very high velocities
at small distances from the star by magnetic pressure force above the surface
of the star. Exploratory 3D simulations show that conical outflows are
symmetric about rotational axis of the disk even if magnetic dipole is
significantly misaligned. Conical outflows and axial jets may appear in
different types of young stars including Class I young stars, classical T Tauri
stars, and EXors.
