The extinction curves of star-forming regions from z=0.1 to 6.7 using
  GRB afterglow spectroscopy
  GRB afterglows are well suited to extinction studies due to their brightness,
simple power-law spectra and the occurrence of GRBs in distant star forming
galaxies. In this paper we present results from the SED analysis of a sample of
41 GRB afterglows, from X-ray to NIR wavelengths. This is the largest sample of
extinction curves outside the Local Group and, to date, the only extragalactic
sample of absolute extinction curves based on spectroscopy. Visual extinction
correlation with HI column density as well as total and gas-phase metal column
density are examined. Approximately half the sample require a cooling break
between the optical and X-ray regimes. The broken power-law SEDs show an
average change in the spectral index of delta_beta=0.51 with a standard
deviation of 0.02. This is consistent with the expectation from a simple
synchrotron model. Of the sample, 63% are well described by the SMC-type
extinction curve and have moderate or low extinction, with AV<0.65. Almost a
quarter of our sample is consistent with no significant extinction (typically
AV<0.1). The 2175AA extinction bump is detected unequivocally in 7% of our
sample (3 GRBs), which all have A_V>1.0. We find an anti-correlation between
gas-to-dust ratio and metallicity consistent with the Local Group relation. Our
metals-to-dust ratios derived from the soft X-ray absorption are always larger
(3-30 times) than the Local Group value, which may mean that GRB hosts may be
less efficient at turning their metals into dust. However, we find that gas,
dust, and metal column densities are all likely to be influenced by
photo-ionization and dust destruction effects from the GRB. [abridged]
