  The origin of the observed variability of the gas-phase D/H ratio in the
local interstellar medium is still debated, and in particular the role of
deuterium depletion onto dust grains. Here we extend the study of the
relationship between deuterium and titanium, a refractory species and tracer of
elemental depletion, and explore other relationships. We have acquired high
resolution spectra for nine early-type stars using the VLT/UVES spectrograph,
and detected the absorption lines of interstellar TiII. Using a weighted
orthogonal distance regression (ODR) code and a special method to treat non
symmetric errors, we compare the TiII columns with the corresponding HI, DI and
also OI columns. We perform in parallel the same comparisons for available FeII
data. We find a significant correlation between TiII/HI and D/H in our data
set, and, when combined with published results, we confirm and better constrain
a previously published trend and extend it to low HI columns. We exclude
uncertainties in HI and OI columns as the main contributor to the derived
metals-deuterium correlations by showing that the TiII/HI ratio is positively
correlated with DI/OI. We find a similar correlation between FeII/HI and
DI/OI.The TiII gradients are similar or slightly smaller than for FeII, while
one would expect larger variations on the basis of the higher condensation
temperature of titanium. However we argue that ionisation effects introduce
biases that affect iron and not titanium and may explain the gradient
similarity. We find a less significant negative correlation between the TiII/DI
ratio and the hydrogen column, possibly a sign of different evaporation of D
and metals according to the cloud properties.
