23 pages, 22 postscript figues, submitted to Phys. Rev. D - P. Grenier aussi au LPCThe e+e- -> p anti-p cross section is determined over a range of p anti-p masses, from threshold to 4.5 GeV/c^2, by studying the e+e- -> p anti-p gamma process. The data set corresponds to an integrated luminosity of 232 fb^-1, collected with the BABAR detector at the PEP-II storage ring, at an e+e- center-of-mass energy of 10.6 GeV. The mass dependence of the ratio of electric and magnetic form factors, |G_E/G_M|, is measured for p anti-p masses below 3 GeV/c^2; its value is found to be significantly larger than 1 for masses up to 2.2 GeV/c^2. We also measure J/psi -> p anti-p and psi(2S) -> p anti-p branching fractions and set an upper limit on Y(4260) -> p anti-p production and decay
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