In order to characterize the electronic structure and study the growth in the monolayer coverage range of K, Rb, and Cs on a cooled sample of highly oriented pyrolytic graphite photoemission spectra are recorded for valence and core electrons and for a final state populated by secondaries. For all three metals a low coverage phase with dispersed adatoms is replaced above a submonolayer coverage threshold by a condensed phase in co-existence with the dispersed phase. The condensate may consist of adsorbed rather than subsurface monolayer islands as we suggested in a previous study of K/graphite based on less extensive data ͓M. Breitholtz et al., Phys. Rev. B 66, 153401 ͑2002͔͒. The revision has led to a different interpretation of the unusual coverage dependence observed for the secondary line, common for the three metals, on which the previous suggestion was partly based. Also common is an energy band, which extends around 0.5 eV below the Fermi level, which we ascribe to alkali metal valence electrons. The dispersion, studied for K, shows that the band accommodates around 0.5 electrons per alkali metal atom. The remaining part of the alkali valence electron is not accounted for by the charge transfer to the substrate estimated from the energy shifts of graphite states. An unexpected observation made for K/graphite at 85 eV photon energy while recording the K 3p line is that intense synchrotron radiation can cause rapid and significant changes of the sample that are not due to desorption of K atoms.