  Semi-analytical models of disk outflows have successfully described
magnetically-driven, self-confined super-Alfv\'enic jets from near Keplerian
accretion disks. These Jet Emitting Disks are possible for high levels of disk
magnetization $\mu$ defined as $\mu=2/\beta$ where beta is the usual plasma
parameter. In near-equipartition JEDs, accretion is supersonic and jets carry
away most of the disk angular momentum. However, these solutions prove
difficult to compare with cutting edge numerical simulations, for the reason
that numerical simulations show wind-like outflows but in the domain of small
magnetization. In this work, we present for the first time self-similar
isothermal solutions for accretion-ejection structures at small magnetization
levels. We elucidate the role of MRI-like structures in the acceleration
processes that drive this new class of solutions. The disk magnetization $\mu$
is the main control parameter: massive outflows driven by the pressure of the
toroidal magnetic field are obtained up to $\mu \sim 10^{-2}$, while more
tenuous centrifugally-driven outflows are obtained at larger $\mu$ values. The
generalized parameter space and the astrophysical consequences are discussed.
We believe that these new solutions could be a stepping stone in understanding
the way astrophysical disks drive either winds or jets. Defining jets as
self-confined outflows and winds as uncollimated outflows, we propose a simple
analytical criterion based on the initial energy content of the outflow, to
discriminate jets from winds. We show that jet solution are achieved at all
magnetization level, while winds could be obtained only in weakly magnetized
disks that feature heating.
