  We update our earlier results regarding detection of $gg\to b\anti b h\to 4b$
($h=h^0,H^0,A^0$) to incorporate the very high $b$-tagging efficiencies and
purities that are now anticipated at the LHC. New results for the Tev$^*$ are
given, and indicate substantial potential for these modes. The complementarity
of the $H^0\to h^0h^0 \to 4b$ final state mode is illustrated for the LHC. The
latest radiative corrections to the Higgs sector are incorporated.
