We present an investigation of the decays B(0) -> Lambda(+)(c)(p) over bar and B(-) -> Lambda(+)(c)(p) over bar pi(-) based on 383 X 10(6)Y(4S) -> B (B) over bar decays recorded with the BABAR detector. We measure the branching fractions of these decays; their ratio is B(B(-) -> Lambda(+)(c)(p) over bar pi(-))/B((B) over bar (0) -> Lambda(+)(c)(p) over bar) = 15.4 +/- 1.8 +/- 0.3. The B(-) -> Lambda(+)(c)(p) over bar pi(-) process exhibits an enhancement at the Lambda(+)(c)(p) over bar threshold and is a laboratory for searches for excited charm baryon states. We observe the resonant decays B(-) -> Sigma(c)(2455)(0)(p) over bar and B(-) -> Sigma(c)(2800)(0)(p) over bar but see no evidence for B(-) -> Sigma(c)(2520)(0)(p) over bar. This is the first observation of the decay B(-) -> Sigma(c)(2800)(0)(p) over bar; however, the mass of the observed excited Sigma(0)(c) state is (2846 +/- 8 +/- 10) MeV/c(2), which is somewhat inconsistent with previous measurements. Finally, we examine the angular distribution of the B(-) -> Sigma(c)(2455)(0)(p) over bar decays and measure the spin of the Sigma(c)(2455)(0) baryon to be 1/2, as predicted by the quark model.