The addition of boron to GaAs nanowires grown by self-catalyzed molecular beam epitaxy was found to have a strong effect on the nanowire morphology, with axial growth greatly reduced as the nominal boron concentration was increased. Transmission electron microscopy measurements show that the Ga catalyst droplet was unintentionally consumed during growth. Concurrent radial growth, a rough surface morphology and tapering of nanowires grown under boron flux suggest that this droplet consumption is due to reduced Ga adatom diffusion on the nanowire sidewalls in the presence of boron. Modelling of the nanowire growth puts the diffusion length of Ga adatoms under boron flux at around 700-1000 nm. Analyses of the nanowire surfaces show regions of high boron concentration, indicating the surfactant nature of boron in GaAs.