With a sample of 232×106 Υ(4S)→BB̅ events collected with the BABAR detector, we study the decays of B mesons to pp̅ h final states, where h=π+, KS0, K*0, or K*+. We report evidence for the B0→pp̅ K*0 decay, with a branching fraction (1.47±0.45(stat)±0.40(syst))×10-6, and for the B+→ηcK*+ decay, with the branching fraction of B(B+→ηcK*+)×B(ηc→pp̅ )=(1.57-0.45+0.56(stat)-0.36+0.46(syst))×10-6, and provide improved measurements of the branching fractions of the other modes of this type. We also report the measurements of the charge asymmetry consistent with zero in the B+→pp̅ π+, B0→pp̅ K*0, and B+→pp̅ K*+ modes. No evidence is found for the pentaquark candidate Θ+ in the mass range 1.52 to 1.55 GeV/c2, decaying into pKS0, or the glueball candidate fJ(2220) in the mass range 2.2<mpp̅ <2.4 GeV/c2, and branching fraction limits are established for both at the 10-7 level.