  Based on recent improvements of the supernova electron antineutrino emission
model, we update the limit on neutrino mass from the SN1987A data collected by
Kamiokande-II, IMB and Baksan. We derive the limit of 5.8 eV at 95 % CL, that
we show to be remarkably insensitive to the astrophysical uncertainties. Also
we evaluate the ultimate mass sensitivity of this method for a detector like
Super-Kamiokande. We find that the bound lies in the sub-eV region, 0.8 eV at
95 % CL being a typical outcome, competitive with the values that are presently
probed in laboratory. However, this bound is subject to strong statistical
fluctuations, correlated to the characteristics of the first few events
detected. We briefly comment on the prospects offered by future detectors.
