The e+e-→pp̄ cross section is determined over a range of pp̄ masses, from threshold to 4.5GeV/c2, by studying the e+e-→pp̄γ process. The data set corresponds to an integrated luminosity of 232fb-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, |GE/GM|, is measured for pp̄ masses below 3GeV/c2; its value is found to be significantly larger than 1 for masses up to 2.2GeV/c2. We also measure J/ψ→pp̄ and ψ(2S)→pp̄ branching fractions and set an upper limit on Y(4260)→pp̄ production and decay. © 2006 The American Physical Society.