Abstract: We report measurements of partial branching fractions for inclusive charmless semileptonic B decays (B) over bar -> X(u)l (v) over bar and the determination of the Cabibbo-Kobayashi-Maskawa (CKM) matrix element vertical bar V-ub vertical bar. The analysis is based on a sample of 467 x 10(6) Y(4S) -> B (B) over bar decays recorded with the BABAR detector at the PEP- II e(+)e(-) storage rings. We select events in which the decay of one of the B mesons is fully reconstructed and an electron or a muon signals the semileptonic decay of the other B meson. We measure partial branching fractions Delta B in several restricted regions of phase space and determine the CKM element vertical bar V-ub vertical bar based on different QCD predictions. For decays with a charged lepton momentum p(l)* > 1.0 GeV in the B meson rest frame, we obtain Delta B = (1.80 +/- 0.13(stat) +/- 0.15(sys) +/- 0.02(theo)) x 10(-3) from a fit to the two-dimensional M-X – q(2) distribution. Here, M-X refers to the invariant mass of the final state hadron X and q(2) is the invariant mass squared of the charged lepton and neutrino. From this measurement we extract vertical bar V-ub vertical bar = (4.33 +/- 0.24(exp) +/- 0.15(theo)) x 10(-3) as the arithmetic average of four results obtained from four different QCD predictions of the partial rate. We separately determine partial branching fractions for (B) over bar (0) and B- decays and derive a limit on the isospin breaking in (B) over bar -> X(u)l (v) over bar decays.