  We present the results of hydrodynamic simulations examining migration and
growth of planets embedded in self-gravitating circumbinary discs. The binary
star parameters are chosen to mimic those of the Kepler-16, -34 and -35
systems; the aim of this study is to examine the role of disc mass in
determining the stopping locations of migrating planets at the edge of the
cavity created by the central binary. Disc self-gravity can cause significant
shrinkage of the cavity for disc masses in excess of 5--10 $\times$ the minimum
mass solar nebula model. Planets forming early in the disc lifetime can migrate
through the disc and stall at locations closer to the central star than is
normally the case for lower mass discs, resulting in closer agreement between
simulated and observed orbital architecture. The presence of a planet orbiting
in the cavity of a massive disc can prevent the cavity size from expanding to
the size of a lower mass disc. As the disc mass reduces over long time scales,
this indicates that circumbinary planet systems retain memory of their initial
conditions. Our simulations produce planetary orbits in good agreement with
Kepler-16b without the need for self-gravity; Kepler-34 analogue systems
produce wide and highly eccentric cavities, and self-gravity improves the
agreement between simulations and data. Kepler-35b is more difficult to explain
in detail due to it's relatively low mass, which results in the simulated
stopping location being at a larger radius than that observed.
