We study the balance in dynamical support of 384 galaxies with stellar kinematics out to >1.5R_e in the Sydney AAO Multi-object Integral Field (SAMI) Galaxy Survey. We present radial dynamical profiles of the local rotation dominance parameter, V/sigma, and local spin, lambda_loc. Although there is a broad range in amplitude, most kinematic profiles monotonically increase across the probed radial range. We do not find many galaxies with kinematic transitions such as those expected between the inner in-situ and outer accreted stars within the radial range probed. We compare the V/sigma gradient and maximum values to the visual morphologies of the galaxies to better understand the link between visual and kinematic morphologies. We find that the radial distribution of dynamical support in galaxies is linked to their visual morphology. Late-type systems have higher rotational support at all radii and steeper V/sigma gradients compared to early-type galaxies. We perform a search for embedded discs, which are rotationally supported discy structures embedded within large scale slowly or non-rotating structures. Visual inspection of the kinematics reveals at most three galaxies (out of 384) harbouring embedded discs. This is more than an order of magnitude fewer than the observed fraction in some local studies. Our tests suggest that this tension can be attributed to differences in the sample selection, spatial sampling and beam smearing due to seeing.
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