The probability distribution function of column density (N-PDF) serves as a powerful tool to characterise the various physical processes that influence the structure of molecular clouds. Studies that use extinction maps or H2 column-density maps (N) that are derived from dust show that star-forming clouds can best be characterised by lognormal PDFs for the lower N range and a power-law tail for higher N, which is commonly attributed to turbulence and self-gravity and/or pressure, respectively. The slopes of the power-law tails of the CS, N2H+, and dust PDFs are -1.6, -1.4, and -2.3, respectively, and are thus consistent with free-fall collapse of filaments and clumps. A quasi static configuration of filaments and clumps can also possibly account for the observed N-PDFs, providing they have a sufficiently condensed density structure and external ram pressure by gas accretion is provided. The somehow flatter slopes of N2H+ and CS can reflect an abundance change and/or subthermal excitation at low column densities.