Measurement of the B{sup 0}{yields}{pi}{sup -}l{sup +}{nu} and B{sup +}{yields}{eta}(')l{sup +}{nu} branching fractions, the B{sup 0}{yields}{pi}{sup -}l{sup +}{nu} and B{sup +}{yields}{eta}l{sup +}{nu} form-factor shapes, and determination of |V{sub ub}|

We report the results of a study of the exclusive charmless semileptonic decays, B{sup +}{yields}{eta}(')l{sup +}{nu} and B{sup 0}{yields}{pi}{sup -}l{sup +}{nu}, undertaken with approximately 464x10{sup 6} BB pairs collected at the {Upsilon}(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{sup +}{yields}{eta}l{sup +}{nu} and B{sup 0}{yields}{pi}{sup -}l{sup +}{nu} decays in three and 12 bins of q{sup 2}, respectively, from which we extract the f{sub +}(q{sup 2}) form-factor shapes and the total branching fractions B(B{sup +}{yields}{eta}l{sup +}{nu})=(0.36{+-}0.05{sub stat}{+-}0.04{sub syst})x10{sup -4} and B(B{sup 0}{yields}{pi}{sup -}l{sup +}{nu})=(1.42{+-}0.05{sub stat}{+-}0.07{sub syst})x10{sup -4}. We also measure B(B{sup +}{yields}{eta}'l{sup +}{nu})=(0.24{+-}0.08{sub stat}{+-}0.03{sub syst})x10{sup -4}. We obtain values for the magnitude of the CKM matrix element |V{sub ub}| using three different QCD calculations.