Measurement of the B^{0}→π^{-}l^{+}ν and B^{+}→η^{(′)}l^{+}ν branching fractions, the B^{0}→π^{-}l^{+}ν and B^{+}→ηl^{+}ν form-factor shapes, and determination of |V_{ub}|

We report the results of a study of the exclusive charmless semileptonic decays, B+→η(′)l+ν and B0→π-l+ν, undertaken with approximately 464×106 BB̅ pairs collected at the Υ(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with a loose neutrino reconstruction technique. We obtain partial branching fractions for B+→ηl+ν and B0→π-l+ν decays in three and 12 bins of q2, respectively, from which we extract the f+(q2) form-factor shapes and the total branching fractions B(B+→ηl+ν)=(0.36±0.05stat±0.04syst)×10-4 and B(B0→π-l+ν)=(1.42±0.05stat±0.07syst)×10-4. We also measure B(B+→η′l+ν)=(0.24±0.08stat±0.03syst)×10-4. We obtain values for the magnitude of the CKM matrix element |Vub| using three different QCD calculations.