  We present updated results on time-dependent CP-violating asymmetries in
neutral B decays to several CP eigenstates. The measurements use a data sample
of about 62 million Upsilon(4S) --> B anti-B decays collected between 1999 and
2001 by the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC.
In this sample we study events in which one neutral B meson is fully
reconstructed in a final state containing a charmonium meson and the flavor of
the other neutral B meson is determined from its decay products. The amplitude
of the CP-violating asymmetry, which in the Standard Model is proportional to
sin2beta, is derived from the decay time distributions in such events. We
measure sin2beta = 0.75 +/- 0.09 (stat) +/- 0.04 (syst) and |\lambda| = 0.92
+/- 0.06 (stat) +/- 0.02 (syst). The latter is consistent with the Standard
Model expectation of no direct CP violation. These results are preliminary.
