We use measurements of the H i content, stellar mass and star formation rates (SFRs) in ~190 massive galaxies with M* > 1010 M., obtained from the GALEX (Galaxy Evolution Explorer) Arecibo SDSS (Sloan Digital Sky Survey) survey described in Paper I to explore the global scaling relations associated with the bin-averaged ratio of the SFR over the H i mass (i.e. ΣSFR/ΣMHi), which we call the H i-based star formation efficiency (SFE). Unlike the mean specific star formation rate (sSFR), which decreases with stellar mass and stellar mass surface density, the SFE remains relatively constant across the sample with a value close to SFE = 10-9.5 yr-1 (or an equivalent gas consumption time-scale of ~3 × 109 yr). Specifically, we find little variation in SFE with stellar mass, stellar mass surface density, NUV -r colour and concentration (R90/R50). We interpret these results as an indication that external processes or feedback mechanisms that control the gas supply are important for regulating star formation in massive galaxies. An investigation into the detailed distribution of SFEs reveals that approximately 5 per cent of the sample shows high efficiencies with SFE > 10-9 yr-1, and we suggest that this is very likely due to a deficiency of cold gas rather than an excess SFR. Conversely, we also find a similar fraction of galaxies that appear to be gas-rich for their given sSFR, although these galaxies show both a higher than average gas fraction and lower than average sSFR. Both of these populations are plausible candidates for 'transition' galaxies, showing potential for a change (either decrease or increase) in their sSFR in the near future. We also find that 36 ± 5 per cent of the total H i mass density and 47 ± 5 per cent of the total SFR density are found in galaxies with M. > 1010 M.. © 2010 The Authors. Journal compilation © 2010 RAS.