We present abundances of Fe , Na , and O for 1409 red giant stars in 15 galactic globular clusters ( GCs ) , derived from the homogeneous analysis of high-resolution FLAMES/GIRAFFE spectra . Combining the present data with results from our FLAMES/UVES spectra and from previous studies within the project , we obtained a total sample of 1958 stars in 19 clusters , the largest and most homogeneous database of this kind to date . The programme clusters cover a range in metallicity from [ Fe/H ] = -2.4 dex to [ Fe/H ] = -0.4 dex , with a wide variety of global parameters ( morphology of the horizontal branch , mass , concentration , etc . ) . For all clusters we find the Na-O anticorrelation , the classical signature of the operation of proton-capture reactions in H-burning at high temperature in a previous generation of more massive stars that are now extinct . Using quantitative criteria ( from the morphology and extension of the Na-O anticorrelation ) , we can define three different components of the stellar population in GCs . We separate a primordial component ( P ) of first-generation stars , and two components of second-generation stars , that we name intermediate ( I ) and extreme ( E ) populations from their different chemical composition . The P component is present in all clusters , and its fraction is almost constant at about one third . The I component represents the bulk of the cluster population . On the other hand , E component is not present in all clusters , and it is more conspicuous in some ( but not in all ) of the most massive clusters . We discuss the fractions and spatial distributions of these components in our sample and in two additional clusters ( MÂ 3=NGCÂ 5272 and MÂ 13=NGC6205 ) with large sets of stars analysed in the literature . We also find that the slope of the anti-correlation ( defined by the minimum O and maximum Na abundances ) changes from cluster-to-cluster , a change that is represented well by a bilinear relation on cluster metallicity and luminosity . This second dependence suggests a correlation between average mass of polluters and cluster mass .