  We present improved measurements of the branching fractions and CP
asymmetries in the two-body decays B0 --> pi0 pi0, B0 --> K0 pi0 and B0 --> K+
pi- as well as the quasi two-body B0 --> K_1(1270)+ pi- and B0 --> K_1(1400)+
pi- decays. These updated measurements are made using the complete set of BABAR
data taken at the Y(4S) resonance, collected between 1999 and 2007 at the
PEP-II collider at SLAC.
