We study the e + e − → Λ ¯¯¯ Λ γ , Λ ¯¯¯ Σ 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 − → Λ ¯¯¯ Λ , Λ ¯¯¯ Σ 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, | G E / G M | , is measured for e + e − → Λ ¯¯¯ Λ , and limits on the relative phase between Λ form factors are obtained. We also measure the J / ψ → Λ ¯¯¯ Λ , Σ 0 ¯¯¯ Σ 0 , and ψ ( 2 S ) → Λ ¯¯¯ Λ branching fractions.