The parameter A +, defined as the area enclosed between the cumulative radial distribution of blue straggler stars (BSSs) and that of a reference population, is a powerful indicator of the level of BSS central segregation. As part of the Hubble Space Telescope UV Legacy Survey of Galactic globular clusters (GCs), here we present the BSS population and the determination of A + in 27 GCs observed out to about one half-mass radius. In combination with 21 additional clusters discussed in a previous paper, this provides us with a global sample of 48 systems (corresponding to ∼32% of the Milky Way GC population), for which we find a strong correlation between A + and the ratio of cluster age to the current central relaxation time. Tight relations have also been found with the core radius and the central luminosity density, which are expected to change with the long-term cluster dynamical evolution. An interesting relation is emerging between A + and the ratio of the BSS velocity dispersion relative to that of main sequence turn-off stars, which measures the degree of energy equipartition experienced by BSSs in the cluster. These results provide further confirmation that BSSs are invaluable probes of GC internal dynamics and that A + is a powerful dynamical clock.