  We study the structure of thick discs in extraordinary depth by reaching a
surface brightness limit of $\mu_{r_{\rm deep}} \sim$28.5$-$29~mag
arcsec$^{-2}$ with combined $g$,$r$,$i$ band images from the IAC Stripe 82
Legacy Project. We present the characterisation of the thick discs in a sample
of five edge-on galaxies. A study of the radial and vertical surface brightness
profiles is presented by comparing our data with point spread function (PSF)
deconvolved models. Our method begins with an analysis of the background and
masking processes. Then we consider the effects of the PSF through galaxy
modelling. The galaxy disc components are fitted considering that the thin and
thick discs are two stellar fluids that are gravitationally coupled in
hydrostatic equilibrium. We find that effects due to the PSF are significant
when low surface brightness is reached, especially in the vertical profiles,
but it can be accounted for by careful modelling. The galaxy outskirts are
strongly affected by the faint wings of the PSF, mainly by PSF-redistributed
light from the thin disc. This is a central problem for ultra-deep imaging. The
thick-disc component is required to reach satisfactory fit results in the more
complex galaxies in our sample, although it is not required for all galaxies.
When the PSF is ignored, the brightness of these structures may be
overestimated by up to a factor of $\sim$4. In general, our results are in good
agreement with those of previous works, although we reach deeper surface
brightness levels, so that the PSF effects are stronger. We obtain scale
heights and mass ratios of thin and thick discs ($z_{{\rm t}}$, $z_{{\rm T}}$,
and $M_{{\rm T}}/M_{{\rm t}}$), which provide excellent agreement with previous
studies. Our small initial sample provides evidence for aspects of a wide
variety of formation theories for the thick discs in disc galaxies.
