We study the following charmless baryonic three-body decays of B mesons: B+-> p (Lambda) over bar gamma, B+-> p (Lambda) over bar pi(0), and B-0 -> p (Lambda) over bar pi(-). The partial branching fractions as a function of the baryon-antibaryon mass and the polar angle distributions of the proton in the baryon-antibaryon system are presented. This study includes the first observation of B+-> p (Lambda) over bar pi(0), which is measured to have a branching fraction of (3.00(-0.53)(+0.61)+/- 0.33)x10(-6). We also set upper limits on branching fractions of the two-body decays B-0 -> p (Sigma) over bar (*-), B-0 ->Delta(0)(Lambda) over bar, B+-> p (Sigma) over bar (*0), and B+->Delta(+)(Lambda) over bar at the 90% confidence level. These results are obtained from a 414 fb(-1) data sample collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider.