The formation of stars is inextricably linked to the structure of their parental molecular clouds. Here we take a number of nearby giant molecular clouds (GMCs) and analyse their column density and mass distributions. This investigation is based on four new all-sky median colour excess extinction maps determined from 2MASS. The four maps span a range of spatial resolution of a factor of eight. This allows us to determine cloud properties at a common spatial scale of 0.1pc, as well as to study the scale dependence of the cloud properties. We find that the low column density and turbulence dominated part of the clouds can be well fit by a log-normal distribution. However, above a universal extinction threshold of 6.0 pm 1.5mag A_V there is excess material compared to the log-normal distribution in all investigated clouds. This material represents the part of the cloud that is currently involved in star formation, and thus dominated by gravity. Its contribution to the total mass of the clouds ranges over two orders of magnitude from 0.1 to 10%. This implies that our clouds sample various stages in the evolution of GMCs. Furthermore, we find that the column density and mass distributions are extremely similar between clouds if we analyse only the high extinction material. On the other hand, there are significant differences between the distributions if only the low extinction, turbulence dominated regions are considered. This shows that the turbulent properties differ between clouds depending on their environment. However, no significant influence on the predominant mode of star formation (clustered or isolated) could be found. Furthermore, the fraction of the cloud actively involved in star formation is only governed by gravity, with the column density and mass distributions not significantly altered by local feedback processes.
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