The e(+)e(-) -> p (p) over bar cross section is determined over a range of p (p) over bar masses, from threshold to 4.5 GeV/c(2), by studying the e(+)e(-)-> p (p) over bar 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, vertical bar G(E)/G(M)vertical bar, is measured for p (p) over bar 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 (p) over bar and psi(2S) -> p (p) over bar branching fractions and set an upper limit on Y(4260) -> p (p) over bar production and decay.