  Whenever in a classical accretion disk the thin disk approximation fails
interior to a certain radius, a transition from Keplerian to radial infalling
trajectories should occur. We show that this transition is actually expected to
occur interior to a certain critical radius, provided surface density profiles
are steeper than $\Sigma(R) \propto R^{-1/2}$, and further, that it probably
corresponds to the observationally inferred phenomena of thick hot walls
internally limiting the extent of many stellar accretion disks. Infalling
trajectories will lead to the convergent focusing and concentration of matter
towards the very central regions, most of which will simply be swallowed by the
central object. We show through a perturbative hydrodynamical analysis, that
this will naturally develop a well collimated pair of polar jets. A first
analytic treatment of the problem described is given, proving the feasibility
of purely hydrodynamical mechanisms of astrophysical jet generation. The purely
hydrodynamic jet generation mechanism explored here complements existing ideas
focusing on the role of magnetic fields, which probably account for the
large-scale collimation and stability of jets.
