  Observations of jets from young stellar objects reveal the asymmetric
outflows from some sources. A large set of $2.5$D MHD simulations has been
carried out for axisymmetric viscous/diffusive disc accretion to rotating
magnetized stars for the purpose of assessing the conditions where the outflows
or jets are asymmetric relative to the equatorial plane. We consider initial
magnetic fields that are symmetric about the equatorial plane and consist of a
radially distributed field threading the disc (disc-field) and a stellar dipole
field.({\bf 1}). For pure disc-fields the symmetry or asymmetry of the outflows
is affected by the midplane plasma $\beta$ of the disc (where $\beta$ is the
ratio of the plasma pressure to the magnetic pressure). For the low density
discs with small plasma $\beta$ values, outflows are observed to be symmetric
to within $10\%$ over timescales of hundreds of inner disc orbits. For the
denser higher $\beta$ discs, the coupling of the upper and lower coronal
plasmas is broken, and quasi-periodic field motion in the two hemispheres
becomes different. This asymmetry leads to asymmetric episodic outflows. ({\bf
2.}) Accreting stars with a stellar dipole field and no disc-field exhibit
episodic, two component outflows - a magnetospheric wind and an inner disc wind
from somewhat larger radial distances. Both are characterized by similar
velocity profiles but the magnetospheric wind has densities $\gtrsim 10$ times
that of the disc wind. ({\bf 3}.)Adding a disc-field parallel to the stellar
dipole field acts to enhance the magnetospheric winds but suppress the disc
wind. ({\bf 4}.) In contrast, adding a disc-field which is anti-parallel to the
stellar dipole field in the disc acts to suppress the magnetospheric and disc
winds. Our simulations reproduce some key features of observations of
asymmetric outflows of T Tauri stars.
