  In most debris discs, dust grain dynamics is strongly affected by stellar
radiation pressure. As this mechanism is size-dependent, we expect dust grains
to be spatially segregated according to their sizes. However, because of the
complex interplay between radiation pressure, collisions and dynamical
perturbations, this spatial segregation of the particle size distribution (PSD)
has proven difficult to investigate with numerical models. We propose to
explore this issue using a new-generation code that can handle some of the
coupling between dynamical and collisional effects. We investigate how PSDs
behave in both unperturbed discs "at rest" and in discs pertubed by planetary
objects. We use the DyCoSS code of Thebault(2012) to investigate the coupled
effect of collisions, radiation pressure and dynamical perturbations in systems
having reached a steady state. We consider 2 setups: a narrow ring perturbed by
an exterior planet, and an extended disc into which a planet is embedded. For
both setups we consider an additional unperturbed case with no planet. We also
investigate how possible spatial size segregation affect disc images at
different wavelengths. We find that PSDs are always strongly spatially
segregated. The only case for which they follow a standard dn/dr = C.r**(-3.5)
law is for an unperturbed narrow ring, but only within the parent body ring
itself. For all other configurations, the PSD can strongly depart from such
power laws and have strong spatial gradients. As an example, the geometrical
cross section of the disc is rarely dominated by the smallest grains on bound
orbits, as it is expected to be in standard PSDs in s**q with q<-3. Although
the exact profiles and spatial variations of PSDs are a complex function of the
considered set-up, we are however able to derive some robust results that
should be useful for image-or-SED-fitting models of observed discs.
