In this paper we compute rest-frame extinctions for the afterglows of a sample of gamma-ray bursts complete in redshift. The selection criteria of the sample are based on observational high-energy parameters of the prompt emission and therefore our sample should not be biased against dusty sight-lines. It is therefore expected that our inferences hold for the general population of gamma-ray bursts. Our main result is that the optical/near-infrared extinction of gamma-ray burst afterglows in our sample does not follow a single distribution. 87% of the events are absorbed by less than 2 mag, and 50% suffer from less than 0.3-0.4 mag extinction. The remaining 13% of the afterglows are highly absorbed. The true percentage of gamma-ray burst afterglows showing high absorption could be even higher since a fair fraction of the events without reliable redshift measurement are probably part of this class. These events may be due to highly dusty molecular clouds/star forming regions associated with the gamma-ray burst progenitor or along the afterglow line of sight, and/or to massive dusty host galaxies. No clear evolution in the dust extinction properties is evident within the redshift range of our sample, although the largest extinctions are at z~1.5-2, close to the expected peak of the star formation rate. Those events classified as dark are characterized, on average, by a higher extinction than typical events in the sample. A correlation between optical/near-infrared extinction and hydrogen-equivalent column density based on X-ray studies is shown although the observed NH appears to be well in excess compared to those observed in the Local Group. Dust extinction does not seem to correlate with GRB energetics or luminosity.
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