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tokens: brought by these results on asymmetric jet launching models. Lovelace et al. (2010) , Dyda et al. (2015) and Lii et al. (2014) have all studied the launching of asymmetric outflows from the magnetospheres of rapidly rotating stars in the propeller regime. They find that the presence of a small dipole component leads to the formation of one-sided accretion funnel flows accompanied by episodic outflows in the opposite hemisphere. The dominant direction of ejection changes stochastically on timescales of ≃30–50 inner disk orbital periods. The inclusion of a disk magnetic field does not significantly affect these results ( Dyda et al. 2015 ; Lii et al. 2014 ). On longer timescales, the jets will therefore look essentially symmetric. Such models therefore cannot account for the velocity asymmetry sustained over typically an order of magnitude longer timescales observed in the DO Tau bipolar jet. A more promising scenario is provided by recent numerical works studying the launching of outflows from magnetised disks. If originating from an MHD disk-wind, a difference of a factor 4 in launching radius would account for a difference of a factor 2 in terminal velocities. Alternatively, different lambda values could be achieved between the two surfaces of the disk. The pioneering studies of Fendt Sheikhnezami (2013) and Dyda et al. (2015) , using a simplified α prescription for the disk viscosity, have shown that indeed asymmetric high velocity jets can develop and endure over long lasting timescales, ≃ a few hundred orbital timescales at the inner disk radius, depending on the disk magnetic properties. Bipolar jet velocity asymmetries of up to a factor 2–2.5 are observed in such models. Recent global non-ideal MHD simulations of magnetised disks, including more comprehensive disk microphysics and evolving both hemispheres, have confirmed these early results and shown that pronounced asymmetries between the lower and upper disk halves of the disk can develop and launch asymmetric outflows which persist over timescales of at least 1000 times the orbital period at the inner disk radius ( Béthune et al. 2017 ; Bai 2017 ; Gressel et al. 2020 ; Riols et al. 2020 ). However, most of these recent simulations do not currently include the very central regions of the disk ( r ≤ 1 au) from which the high-velocity jets are launched. 4.3 The origin of jet axis wiggling As seen in Sect. 4.1 , the DO Tau bipolar jet shows a quasi-sinusoidal small amplitude wiggling of its axis. Similar wiggling has been recently revealed at the base of other T Tauri jets (e.g. Dougados et al. 2000 ; Anglada et al. 2007 ; Garufi et al. 2019 ). This wiggling is often interpreted as tracing the dynamical perturbation due to an unseen companion. A companion can induce wiggling of the jet axis in two different ways. The first one is orbital motion of the jet source ( Masciadri Raga 2002 ; hereafter ‘orbital scenario’). Alternatively, a mis-aligned companion can cause retrograde precession