  The pulse morphology of fast radio bursts (FRBs) provides key information in
both understanding progenitor physics and the plasma medium through which the
burst propagates. We present a study of the profiles of 33 bright FRBs detected
by the Australian Square Kilometre Array Pathfinder. We identify seven FRBs
with measureable intrinsic pulse widths, including two FRBs that have been seen
to repeat. In our modest sample we see no evidence for bimodality in the pulse
width distribution. We also identify five FRBs with evidence of millisecond
timescale pulse broadening caused by scattering in inhomogeneous plasma. We
find no evidence for a relationship between pulse broadening and extragalactic
dispersion measure. The scattering could be either caused by extreme turbulence
in the host galaxy or chance propagation through foreground galaxies. With
future high time resolution observations and detailed study of host galaxy
properties we may be able to probe line-of-sight turbulence on gigaparsec
scales.
