We present a 127 x 63-deg(2) extinction map of the Anticentre of the Galaxy, based on < J - H > and < H - K > colour excess maps from the Two-Micron All-Sky Survey. This 8001-deg(2) map with a resolution of 4 arcmin is provided as online material. The colour excess ratio < J-H >/< H -K > is used to determine the power-law index of the reddening law (beta) for individual regions contained in the area (e.g. Orion, Perseus, Taurus, Auriga, Monoceros, Camelopardalis, Cassiopeia). On average we find a dominant value of beta = 1.8 +/- 0.2 for the individual clouds, in agreement with the canonical value for the interstellar medium. We also show that there is an internal scatter of beta values in these regions, and that in some areas more than one dominant beta values are present. This indicates large-scale variations in the dust properties. The analysis of the A(V) values within individual regions shows a change in the slope of the column density distribution with distance. This can be attributed either to a change in the governing physical processes in molecular clouds on spatial scales of about 1 pc or to an A(V) dilution with distance in our map
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