  We report the novel detection of complex high-column density tails in the
probability distribution functions (PDFs) for three high-mass star-forming
regions (CepOB3, MonR2, NGC6334), obtained from dust emission observed with
Herschel. The low column density range can be fit with a lognormal
distribution. A first power-law tail starts above an extinction (Av) of ~6-14.
It has a slope of alpha=1.3-2 for the rho~r^-alpha profile for an equivalent
density distribution (spherical or cylindrical geometry), and is thus
consistent with free-fall gravitational collapse. Above Av~40, 60, and 140, we
detect an excess that can be fitted by a flatter power law tail with alpha>2.
It correlates with the central regions of the cloud (ridges/hubs) of size ~1 pc
and densities above 10^4 cm^-3. This excess may be caused by physical processes
that slow down collapse and reduce the flow of mass towards higher densities.
Possible are: 1. rotation, which introduces an angular momentum barrier, 2.
increasing optical depth and weaker cooling, 3. magnetic fields, 4. geometrical
effects, and 5. protostellar feedback. The excess/second power-law tail is
closely linked to high-mass star-formation though it does not imply a universal
column density threshold for the formation of (high-mass) stars.
