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-Shooters 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.
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