Aims: We present a detailed study of the radial distribution of the multiple populations identified in the Galactic globular cluster ω Cen. Methods: We used both space-based images (ACS/WFC and WFPC2) and ground-based images (FORS1@VLT and WFI@2.2m ESO telescopes) to map the cluster from the inner core to the outskirts ( 20 arcmin). These data sets have been used to extract high-accuracy photometry for the construction of color-magnitude diagrams and astrometric positions of 900 000 stars. Results: We find that in the inner 2 core radii the blue main sequence (bMS) stars slightly dominate the red main sequence (rMS) in number. At greater distances from the cluster center, the relative numbers of bMS stars with respect to rMS drop steeply, out to 8 arcmin, and then remain constant out to the limit of our observations. We also find that the dispersion of the Gaussian that best fits the color distribution within the bMS is significantly greater than the dispersion of the Gaussian that best fits the color distribution within the rMS. In addition, the relative number of intermediate-metallicity red-giant-branch stars (which includes the progeny of the bMS) with respect to the metal-poor component (the progeny of the rMS) follows a trend similar to that of the main-sequence star-count ratio N{bMS}/NrMS. The most metal-rich component of the red-giant branch follows the same distribution as the intermediate-metallicity component. Conclusions: We briefly discuss the possible implications of the observed radial distribution of the different stellar components in ω Cen. Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555, and on observations made with ESO telescopes at La Silla and Paranal Observatories.