  We study the e+e- --> Lambda anti-Lambda gamma, Lambda anti-Sigma0 gamma,
Sigma0 anti-Sigma0 gamma 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- --> Lambda anti-Lambda, Lambda anti-Sigma0, Sigma0 anti-Sigma0 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- -->
Lambda anti-Lambda, and limits on the relative phase between Lambda form
factors are obtained. We also measure the J/psi --> Lambda anti-Lambda, Sigma0
anti-Sigma0 and psi(2S) --> Lambda anti-Lambda branching fractions.
