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Semi-analytical models of disk outflows have successfully describedmagnetically-driven, self-confined super-Alfv\'enic jets from near Keplerianaccretion disks. These Jet Emitting Disks are possible for high levels of diskmagnetization $\mu$ defined as $\mu=2/\beta$ where beta is the usual plasmaparameter. In near-equipartition JEDs, accretion is supersonic and jets carryaway most of the disk angular momentum. However, these solutions provedifficult to compare with cutting edge numerical simulations, for the reasonthat numerical simulations show wind-like outflows but in the domain of smallmagnetization. In this work, we present for the first time self-similarisothermal solutions for accretion-ejection structures at small magnetizationlevels. We elucidate the role of MRI-like structures in the accelerationprocesses that drive this new class of solutions. The disk magnetization $\mu$is the main control parameter: massive outflows driven by the pressure of thetoroidal magnetic field are obtained up to $\mu \sim 10^{-2}$, while moretenuous centrifugally-driven outflows are obtained at larger $\mu$ values. Thegeneralized parameter space and the astrophysical consequences are discussed.We believe that these new solutions could be a stepping stone in understandingthe way astrophysical disks drive either winds or jets. Defining jets asself-confined outflows and winds as uncollimated outflows, we propose a simpleanalytical criterion based on the initial energy content of the outflow, todiscriminate jets from winds. We show that jet solution are achieved at allmagnetization level, while winds could be obtained only in weakly magnetizeddisks that feature heating.

Magnetically-driven jets and winds from weakly magnetized accretion disks