  Cosmological Perturbation Theory (PT) is a useful tool to study the cumulants
of the density and velocity fields in the large scale structure of the
Universe. In Papers I & II of this series we saw that the Spherical Collapse
(SC) model provides with the exact solution to PT at tree-level and gives a
good approximation to the loop corrections (next to leading orders), indicating
negligible tidal effects. Here, we derive predictions for the (smoothed)
cumulants of the velocity divergence field $\theta \equiv \nabla\cdot\vv$ for
an irrotational fluid in the SC model. By comparing with the exact analytic
results by Scoccimarro & Frieman (1996), it is shown that, at least for the
unsmoothed case, the loop corrections to the cumulants of $\theta$ are
dominated by tidal effects. However, most of the tidal contribution seems to
cancel out when computing the hierarchical ratios, $T_J = {<\theta^J>
  / <\theta^2>^{J-1}}$. We also extend the work presented in Papers I & II to
give predictions for the cumulants of the density and velocity divergence
fields in non-flat spaces. In particular, we show the equivalence between the
spherically symmetric solution to the equations of motion in the SC model
(given in terms of the density) and that of the Lagrangian PT approach (in
terms of the displacement field). It is shown that the $\Omega$-dependence is
very weak for both cosmic fields even at one-loop (a 10% effect at most),
except for the overall factor $f(\Omega)$ that couples to the velocity
divergence.
