  Breaks in the surface brightness profiles in the outer regions of galactic
discs are thought to have formed by various internal and external processes,
and by studying the breaks we aim to better understand what processes are
responsible for the evolution of the outer discs. We use a large well-defined
sample to study how common the breaks are, and whether their properties depend
on galaxy stellar mass or observed wavelength. We study radial surface
brightness profiles of 753 galaxies, obtained from the $3.6 \mu m$ images of
the Spitzer Survey of Stellar Structure in Galaxies (S$^4$G), and the
$K_s$-band data from the Near InfraRed S0-Sa galaxy Survey (NIRS0S), covering a
wide range of galaxy morphologies and stellar masses. Optical SDSS or Liverpool
telescope data was used for 480 of these galaxies. We find that in low-mass
galaxies the single exponential discs (Type I) are most common, and that their
fraction decreases with increasing galaxy stellar mass. The fraction of
down-bending (Type II) discs increases with stellar mass, possibly due to more
common occurrence of bar resonance structures. The up-bending (Type III) discs
are also more common in massive galaxies. The observed wavelength affects the
scalelength of the disc of every profile type. Especially the scalelength of
the inner disc of Type II profiles increases from infrared to u-band on average
by a factor of $\sim 2.2$. Consistent with the previous studies, we find that
Type II outer disc scalelengths ($h_o$) in late-type and low-mass galaxies are
shorter in bluer wavelengths, possibly due to stellar radial migration
populating the outer discs with old stars. In Type III discs $h_o$ are larger
in the u-band, hinting to the presence of young stellar population in the outer
disc. While the observed wavelength affects the disc parameters, it does not
significantly affect the profile type in our sample. (Abridged)
