The large majority of extinction sight lines in our Galaxy obey a simple relation depending on one parameter, the total-to-selective extinction coefficient, Rv. Different values of Rv are able to match the whole extinction curve through different environments so characterizing normal extinction curves. In this paper more than sixty curves with large ultraviolet deviations from their best-fit one parameter curve are analyzed. These curves are fitted with dust models to shed light into the properties of the grains, the processes affecting them, and their relations with the environmental characteristics. The extinction curve models are reckoned by following recent prescriptions on grain size distributions able to describe one parameter curves for Rv values from 3.1 to 5.5. Such models, here extended down to Rv=2.0, allow us to compare the resulting properties of our deviating curves with the same as normal curves in a self-consistent framework, and thus to recover the relative trends overcoming the modeling uncertainties. Such curves represent the larger and homogeneous sample of anomalous curves studied so far with dust models. Results show that the ultraviolet deviations are driven by a larger amount of small grains than predicted for lines of sight where extinction depends on one parameter only. Moreover, the dust-to-gas ratios of anomalous curves are lower than the same values for no deviating lines of sight. Shocks and grain-grain collisions should both destroy dust grains, so reducing the amount of the dust trapped into the grains, and modify the size distribution of the dust, so increasing the small-to-large grain size ratio. Therefore, the extinction properties derived should arise along sight lines where shocks and high velocity flows perturb the physical state of the interstellar medium living their signature on the dust properties. (Abridged version)
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