AIMS: To study the structure of nearby (< 500 pc) dense starless and star-forming cores with the particular goal to identify and understand evolutionary trends in core properties, and to explore the nature of Very Low Luminosity Objects (< 0.1 L_sun; VeLLOs). METHODS: Using the MAMBO bolometer array, we create maps unusually sensitive to faint (few mJy per beam) extended (approx. 5 arcmin) thermal dust continuum emission at 1.2 mm wavelength. Complementary information on embedded stars is obtained from Spitzer, IRAS, and 2MASS. RESULTS: Our maps are very rich in structure, and we characterize extended emission features (``subcores) and compact intensity peaks in our data separately to pay attention to this complexity. We derive, e.g., sizes, masses, and aspect ratios for the subcores, as well as column densities and related properties for the peaks. Combination with archival infrared data then enables the derivation of bolometric luminosities and temperatures, as well as envelope masses, for the young embedded stars. CONCLUSIONS: (abridged) Starless and star-forming cores occupy the same parameter space in many core properties; a picture of dense core evolution in which any dense core begins to actively form stars once it exceeds some fixed limit in, e.g., mass, density, or both, is inconsistent with our data. Comparison of various evolutionary indicators for young stellar objects in our sample (e.g., bolometric temperatures) reveals inconsistencies between some of them, possibly suggesting a revision of some of these indicators.
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