  Aims: We derive the probability density functions (PDFs) of column density
for a complete sample of prominent molecular cloud complexes closer than 200
pc. Methods: We derive near-infrared dust extinction maps for 23 molecular
cloud complexes, using the "nicest" colour excess mapping technique and data
from the 2MASS archive. The extinction maps are then used to examine the column
density PDFs in the clouds. Results: The column density PDFs of most molecular
clouds are well-fitted by log-normal functions at low column densities (0.5 mag
< A_v < 3-5 mag). However, at higher column densities prominent, power-law-like
wings are common. In particular, we identify a trend among the PDFs: active
star-forming clouds always have prominent non-log-normal wings. In contrast,
clouds without active star formation resemble log-normals over the whole
observed column density range, or show only low excess of higher column
densities. This trend is also reflected in the cumulative PDFs, showing that
the fraction of high column density material is significantly larger in
star-forming clouds. These observations are in agreement with an evolutionary
trend where turbulent motions are the main cloud-shaping mechanism for
quiescent clouds, but the density enhancements induced by them quickly become
dominated by gravity (and other mechanisms) which is strongly reflected by the
shape of the column density PDFs. The dominant role of the turbulence is
restricted to the very early stages of molecular cloud evolution, comparable to
the onset of active star formation in the clouds.
