Discs no more: the morphology of low-mass simulated galaxies in FIREbox

We study the morphology of hundreds of simulated central galaxies in the stellar mass range [Formula: see text] 10^7.5-10¹¹  [Formula: see text] from the FIREbox cosmological volume. We demonstrate that FIREbox is able to predict a wide variety of morphologies, spanning from disc-dominated objects to spheroidal galaxies supported by stellar velocity dispersion. However, the simulations predict a strong relation between morphology (degree of rotational support) and stellar mass: galaxies comparable to the Milky Way are often disc-dominated while the presence of stellar discs mostly vanishes for dwarfs with [Formula: see text][Formula: see text]. This defines a 'morphology transition' regime for galaxies with [Formula: see text] in which discs become increasingly common, but below which discs are rare. We show that burstiness in the star formation history and the deepening of the gravitational potential strongly correlate in our simulations with this transition regime, with discs forming in objects with lower levels of burstiness in the last [Formula: see text] Gyr and haloes with mass [Formula: see text] and above. While observations support a transition towards thicker discs in the regime of dwarfs, our results are in partial disagreement with observations of at least some largely rotationally supported gas discs in dwarfs with [Formula: see text][Formula: see text]. This study highlights dwarf morphology as a fundamental benchmark for testing future galaxy formation models.