We study the e + e − → ΛΛγ, ΛΣ 0 γ, Σ 0 Σ 0 γ processes using 230 fb −1 of integrated luminosity collected by the BABAR detector at e + e − center-of-mass energy of 10.58 GeV. From the analysis of the baryon-antibaryon mass spectra the cross sections for e + e − → ΛΛ, ΛΣ 0 , Σ 0 Σ 0 are measured in the dibaryon mass range from threshold up to 3 GeV/c 2 . The ratio of electric and magnetic form factors, |GE/GM |, is measured for e + e − → ΛΛ, and limits on the relative phase between Λ form factors are obtained. We also measure the J/ψ → ΛΛ, Σ 0 Σ 0 and ψ(2S) → ΛΛ branching fractions.