  In this third paper in our cloud-collision series, we present the results
from simulations of head-on collisions with a strongly centrally-condensed
initial density profile of $\rm \rho \propto R^{-2}$. We investigate the impact
of these density profiles on the overall evolution of the simulations: the
structures formed, their dynamical evolution, and their star formation
activity. We consider clouds which are globally bound and globally unbound,
leading to three different scenarios -- the collision of a bound cloud with a
bound cloud, the collision of two unbound clouds, or the collision of one cloud
of each type. In all the simulations dense star clusters form before the
collisions occur, and we find that star formation remains confined to these
systems and is little affected by the collisions. If the clouds' are both
initially bound, the collision forms a filamentary structure, but otherwise,
this does not occur. We observe that rotating structures form around the
clusters, but they also form in our non-colliding control simulations, so are
not a consequence of the collisions. Dissipation of kinetic energy in these
simulations is inefficient because of the substructure created in the clouds by
turbulence before the collisions. As a result, although some gas is left bound
in the COM frame, the star clusters formed in the simulations do not become
bound to each other.
