  Blue straggler stars are exotic objects present in all stellar environments
whose nature and formation channels are still partially unclear. They seem to
be particularly abundant in open clusters (OCs), thus offering a unique chance
to tackle these problems statistically.We aim to build up a new and homogeneous
catalogue of blue straggler stars (BSS) in Galactic OCs using Gaia to provide a
more solid assessment of the membership of these stars. We also aim to explore
possible relationships of the straggler abundance with the parent cluster's
structural and dynamical parameters. As a by-product, we also search for
possible yellow straggler stars (YSS), which are believed to be stragglers in a
more advanced evolution stage. We employed photometry, proper motions, and
parallaxes extracted from Gaia DR2 for 408 Galactic star clusters and searched
for stragglers within them after performing a careful membership analysis. The
number of BBS emerging from our more stringent, selection criteria turns out to
be significantly smaller than in previous versions of this catalogue. OCs are
therefore not a preferable environment for these kinds of stars anymore. In
addition, we found that BSS start to appear in clusters with ages larger than
log(t) ~ 8.7 and are therefore absent in very young star clusters.The present
catalogue supersedes the previous ones in several ways: membership assessment,
number of stragglers found, and so forth. The new list includes 897 BSS and 77
YSS candidates in 408 OCs. We expect this catalogue to be the basis for a new
round of studies of BSS and YSS.
