  We report measurements of branching fractions for the decays B --> P l nu,
where P are the pseudoscalar charmless mesons pi-, pi0, eta and eta', based on
348 fb-1 of data collected with the BABAR detector, using B0 and B+ mesons
found in the recoil of a second B meson decaying as B --> D(*) l nu. Assuming
isospin symmetry, we combine pionic branching fractions to obtain B(B0 --> pi-
l+ nu) = (1.54 +/- 0.17(stat) +/- 0.09(syst)) x 10-4; we find 3.2 sigma
evidence of the decay B+ --> eta l+ nu and measure its branching fraction to be
(0.64 +/- 0.20 (stat) +/- 0.03 (syst)) x 10-4, and determine B(B+ --> eta' l+
nu) < 0.47 x 10-4 to 90% confidence level. Using partial branching fractions
for the pionic decays in ranges of the momentum transfer and a recent form
factor calculation, we obtain the magnitude of the Cabibbo-Kobayashi-Maskawa
matrix element |Vub| = (4.0 +/- 0.5(stat) +/- 0.2(syst) +0.7-0.5(theory)) x
10-3.
