  Sub-damped Lyman alpha systems (subDLAs; HI column densities of
19.0<=logN(HI)<20.3) are rarely included in the cosmic HI census performed at
redshifts z>=1.5, yet are expected to contribute significantly to the overall
HI mass budget of the Universe. In this paper, we present a blindly selected
sample of 155 subDLAs found along 100 quasar sightlines (with a redshift path
length X=475) in the XQ-100 survey to investigate the contribution of subDLAs
to the HI mass density of the Universe. The impact of X-Shooter's spectral
resolution on sub-DLA identification is evaluated, and found to be sufficient
for reliably finding absorbers with logN(HI)>=18.9. We compared the
implications of searching for subDLAs solely using HI absorption versus the use
of additional metal lines to confirm the identification, and found that
metal-selection techniques would have missed 75 subDLAs. Using a
bootstrap-Monte Carlo simulation, we computed the column density distribution
function (f(N,X)) and the cosmological HI mass density of subDLAs and compared
with our previous work based on the XQ-100 damped Lyman alpha systems. We do
not find any significant redshift evolution in f(N,X) or cosmological HI mass
density for subDLAs. However, subDLAs contribute 10-20 per cent of the total
cosmological HI mass density measured at redshifts 2<z<5 (agreeing with
previous measurements), and thus have a small but significant contribution to
the HI budget of the Universe.
