We study the stellar mass Tully-Fisher relation ( TFR ; stellar mass versus rotation velocity ) for a morphologically blind selection of emission line galaxies in the field at redshifts 0.1 < z < 0.375 . Kinematics ( \sigma _ { g } , V _ { rot } ) are measured from emission lines in Keck/DEIMOS spectra and quantitative morphology is measured from V- and I-band Hubble images . We find a transition stellar mass in the TFR , \log M _ { * } = 9.5 M _ { \odot } . Above this mass , nearly all galaxies are rotation-dominated , on average more morphologically disk-like according to quantitative morphology , and lie on a relatively tight TFR . Below this mass , the TFR has significant scatter to low rotation velocity and galaxies can either be rotation-dominated disks on the TFR or asymmetric or compact galaxies which scatter off . We refer to this transition mass as the ‘ ‘ mass of disk formation '' , M _ { \mathrm { df } } because above it all star-forming galaxies form disks ( except for a small number of major mergers and highly star-forming systems ) , whereas below it a galaxy may or may not form a disk .