  [Abridged] We analyse the morphological structures in galaxies of the ATLAS3D
sample by fitting a single Sersic profile and decomposing all non-barred
objects (180 of 260 objects) in two components parameterised by an exponential
and a general Sersic function. The aim of this analysis is to look for
signatures of discs in light distributions of nearby early-type galaxies and
compare them to kinematic properties. Using Sersic index from single component
fits for a distinction between slow and fast rotators, or even late- and
early-type galaxies, is not recommended. Assuming that objects with n>3 are
slow rotators (or ellipticals), there is only a 22 per cent probability to
correctly classify objects as slow rotators (or 37 per cent of previously
classified as ellipticals). We show that exponential sub-components, as well as
light profiles fitted with only a single component of a low Sersic index, can
be linked with the kinematic evidence for discs in early-type galaxies. The
median disk-to-total light ratio for fast and slow rotators is 0.41 and 0.0,
respectively. Similarly, the median Sersic indices of the bulge (general Sersic
component) are 1.7 and 4.8 for fast and slow rotators, respectively. Overall,
discs or disc-like structures, are present in 83 per cent of early-type
galaxies which do not have bars, and they show a full range of disk-to-total
light ratios. Discs in early-type galaxies contribute with about 40 per cent to
the total mass of the analysed (non-barred) objects. The decomposition into
discs and bulges can be used as a rough approximation for the separation
between fast and slow rotators, but it is not a substitute, as there is only a
59 per cent probability to correctly recognise slow rotators. Kinematics (i.e.
projected angular momentum) remains the best approach to mitigate the influence
of the inclination effects.
