  We present N-PDFs of 29 Galactic regions obtained from Herschel imaging at
high angular resolution, covering diffuse and quiescent clouds, and those
showing low-, intermediate-, and high-mass star formation (SF), and
characterize the cloud structure using the Delta-variance tool. The N-PDFs are
double-log-normal at low column densities, and display one or two power law
tails (PLTs) at higher column densities. For diffuse, quiescent, and low-mass
SF clouds, we propose that the two log-normals arise from the atomic and
molecular phase, respectively. For massive clouds, we suggest that the first
log-normal is built up by turbulently mixed H2 and the second one by compressed
(via stellar feedback) molecular gas. Nearly all clouds have two PLTs with
slopes consistent with self-gravity, where the second one can be flatter or
steeper than the first one. A flatter PLT could be caused by stellar feedback
or other physical processes that slow down collapse and reduce the flow of mass
toward higher densities. The steeper slope could arise if the magnetic field is
oriented perpendicular to the LOS column density distribution. The first
deviation point (DP), where the N-PDF turns from log-normal into a PLT, shows a
clustering around values of a visual extinction of AV (DP1) around 2-5. The
second DP, which defines the break between the two PLTs, varies strongly. Using
the Delta-variance, we observe that the AV value, where the slope changes
between the first and second PLT, increases with the characteristic size scale
in the variance spectrum. We conclude that at low column densities, atomic and
molecular gas is turbulently mixed, while at high column densities, the gas is
fully molecular and dominated by self-gravity. The best fitting model N-PDFs of
molecular clouds is thus one with log-normal low column density distributions,
followed by one or two PLTs.
