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The authors report the results of a study of the exclusive charmless semileptonic decay, B{sup 0} {yields} {pi}{sup -}{ell}{sup +}{nu}, undertaken with approximately 227 million B{bar B} pairs collected at the {Upsilon}(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. They obtain partial branching fractions in 12 bins of q{sup 2}, the momentum transfer squared, from which they extract the f{sub +}(q{sup 2}) form-factor shape and the total branching fraction {Beta}(B{sup 0} {yields} {pi}{sup -}{ell}{sup +}{nu}) = (1.46 {+-} 0.07{sub stat} {+-} 0.08{sub syst}) x 10{sup -4}. Based on a recent unquenched lattice QCD calculation of the form factor in the range q{sup 2} > 16 GeV{sup 2}/c{sup 4}, they find the magnitude of the CKM matrix element |V{sub ub}| to be (4.1 {+-} 0.2{sub stat} {+-} 0.2{sub syst{sub -0.4}{sup +0.6}FF}) x 10{sup -3}, where the last uncertainty is due to the normalization of the form factor.