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 $β$ of the disc (where $β$ is the ratio of the plasma pressure to the magnetic pressure). For the low density discs with small plasma $β$ values, outflows are observed to be symmetric to within $10\%$ over timescales of hundreds of inner disc orbits. For the denser higher $β$ 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.
