We have used a combination of multiband high-resolution and wide-field ground-based observations to image the Galactic globular cluster M75 (NGC 6864). The extensive photometric sample covers the entire cluster extension, from the very central regions out to the tidal radius, allowing us to determine the center of gravity and to construct the most extended star density profile ever published for this cluster. We also present the first detailed star counts in the very inner regions. The star density profile is well re-produced by a standard King model with core radius r_c ~ 5.4" and intermediate-high concentration c ~ 1.75. The present paper presents a detailed study of the BSS population and its radial distribution. A total number of 62 bright BSSs (with m_F255W < 21, corresponding to m_F555W < 20) has been identified, and they have been found to be highly segregated in the cluster core. No significant upturn in the BSS frequency has been observed in the outskirts of M75, in contrast to several other clusters studied with the same technique. This observational fact is quite similar to what has been found in M79 (NGC 1904) by Lanzoni et al. (2007a). Indeed the BSS radial distributions in the two clusters is qualitatively very similar, even if in M75 the relative BSS frequency seems to decrease significantly faster than in M79: indeed it decreases by a factor of 5 (from 3.4 to 0.7) within 1 r_c. Such evidence indicate that the vast majority of the cluster heavy stars (binaries) have already sunk to the core.

ApJ accepted, 10 pages, 11 figures, 2 tables