Context: Blue stragglers stars (BSS) constitute an ubiquitous population of objects whose origin involves both dynamical and stellar evolution. Aims: In this paper we study the properties of a catalogue of BSS extracted from an homogeneous sample of 56 Galactic globular clusters (GC) observed with Wide-Field Planetary Camera 2 on board of Hubble Space Telescope (WFPC2/HST). Methods: With the purpose of investigating the environmental dependence of the BSS formation mechanisms, we explore possible monovariate relations between the frequency of BSS (divided in different subsamples according to their location with respect to the parent cluster core radius and half-mass radius) and the main parameters of their host GC. We also performed a principal component analysis (PCA) to extract the main parent cluster parameters, which characterise the BSS family. Results: We find that any subpopulation of BSS strongly depends on the luminosity of the cluster, on the extension of the cluster horizontal branch, and on the central velocity dispersion: more luminous clusters and clusters with a smaller central velocity dispersion have a higher BSS frequency. Moreover, we find that clusters having higher mass, higher central densities, and smaller core relaxation timescales have, on average, more luminous BSS. Finally, different dependencies seem to hold for clusters with different integrated luminosity: brighter clusters show a BSS population that depends on the collisional parameter, while BSS in fainter clusters are mostly influenced by the cluster luminosity and the dynamical timescales. The tables with the BSS catalogues, similar to Table [see full text], are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/483/183