HD/H2 as a probe of the roles of gas, dust, light, metallicity and
  cosmic rays in promoting the growth of molecular hydrogen in the diffuse
  interstellar medium
  We modelled recent observations of UV absorption of HD and \HH\ in the Milky
Way and toward damped/sub-damped Lyman alpha systems at z=0.18 and z $>$ 1.7.
N(HD)/N(\HH) ratios reflect the separate self-shieldings of HD and \HH\ and the
coupling introduced by deuteration chemistry. Locally, observations are
explained by diffuse molecular gas with $ 16 \pccc \la$ n(H) $\la 128 \pccc $
if the cosmic-ray ionization rate per H-nucleus \zetaH $= 2\times 10^{-16}\ps$
as inferred from \H3\p\ and OH\p. The dominant influence on N(HD)/N(\HH) is the
cosmic-ray ionization rate with a much weaker downward dependence on n(H) at
Solar metallicity, but dust-extinction can drive N(HD) higher as with N(\HH).
At z $>$ 1.7, N(HD) is comparable to the Galaxy but with 10x smaller N(\HH) and
somewhat smaller N(\HH)/N(H I). Comparison of our Galaxy and the Magellanic
Clouds shows that smaller \HH/H is expected at sub-Solar metallicity and we
show by modelling that HD/\HH\ increases with density at low metallicity,
opposite to the Milky Way. Observations of HD would be explained with higher
n(H) at low metallicity but high-z systems have high HD/\HH\ at metallicity
0.04 $\la$ Z $\la$ 2 Solar. In parallel we trace dust-extinction and
self-shielding effects. The abrupt \HH\ transition to \HH/H $\approx$ 1-10%
occurs mostly from self-shielding although it is assisted by extinction for
n(H) $\la 16 \pccc$. Interior \HH\ fractions are substantially increased by
dust extinction below $\la 32\pccc$. At smaller n(H), \zetaH, small increases
in \HH\ triggered by dust extinction can trigger abrupt increases in N(HD).
