  We perform a structural decomposition of galaxies identified in three
cosmological hydrodynamical simulations by applying Gaussian Mixture Models
(GMMs) to the kinematics of their stellar particles. We study the resulting
disc, bulge, and intra-halo light (IHL) components of galaxies whose host dark
matter haloes have virial masses in the range $M_{200}=10^{11}$--
$10^{15}\,{\rm M_\odot}$. Our decomposition technique isolates galactic discs
whose mass fractions, $f_{\rm disc}$, correlate strongly with common
alternative morphology indicators; for example, $f_{\rm disc}$ is approximately
equal to $\kappa_{{\rm co}}$, the fraction of stellar kinetic energy in
co-rotation. The primary aim of our study, however, is to characterise the IHL
of galaxies in a consistent manner and over a broad mass range, and to analyse
its properties from the scale of galactic stellar haloes up to the
intra-cluster light. Our results imply that the IHL fraction, $f_{\rm IHL}$,
has appreciable scatter and is strongly correlated with galaxy morphology: at
fixed stellar mass, the IHL of disc galaxies is typically older and less
massive than that of spheroids. Above $M_{200}\approx 10^{13}\,{\rm M_\odot}$,
we find, on average, $f_{\rm IHL}\approx 0.45$, albeit with considerable
scatter. The transition radius beyond which the IHL dominates the stellar mass
of a galaxy is roughly $30\,{\rm kpc}$ for $M_{200}\lesssim 10^{12.8}\,{\rm
M_\odot}$, but increases strongly towards higher masses. However, we find that
no alternative IHL definitions -- whether based on the ex-situ stellar mass, or
the stellar mass outside a spherical aperture -- reproduce our
dynamically-defined IHL masses.
