We study the e+e-→ΛΛ̄γ, ΛΣ̄ 0γ, Σ0Σ̄0γ processes using 230fb-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-→ΛΛ̄, ΛΣ̄0, Σ0Σ̄0 are measured in the dibaryon mass range from threshold up to 3GeV/c2. The ratio of electric and magnetic form factors, |GE/GM|, is measured for e+e-→ΛΛ̄, and limits on the relative phase between Λ form factors are obtained. We also measure the J/ψ→ΛΛ̄, Σ0Σ̄0, and ψ(2S)→ΛΛ̄ branching fractions. © 2007 The American Physical Society.