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abstract: 'We show that if 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. Once shears stop, the inner region of radially infalling orbits is naturally expected to be cold. This leads to the divergent focusing and concentration of matter towards the very central regions, most of which will simply be swallowed by the central star. However, if a warm minority component is present, we show through a perturbative hydrodynamical analysis, that this will naturally develop into an extremely well collimated and very fast moving 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 