  Outward migration of massive binary stars or black holes in their
circumbinary disc is often observed in simulations and it is key to the
formation of wide black hole binaries. Using numerical simulations of
Population III (Pop III) star formation, we study the angular momentum of Pop
III binaries and the torques between stars and gas discs to understand the
origin of outward migration and high ellipticity. The outward migration of
protostars is produced by gravitational torques exerted on them by their
circumstellar minidiscs. The minidiscs, on the other hand, migrate outward
mainly by gaining angular momentum by accreting gas from the circumbinary disc.
The angular momentum transfer is most efficient for rapidly accreting
equal-mass binaries, and weaker when the secondary mass is small or the massive
companion evaporates the gas disc via radiative feedback. We conclude that
outward migration and the formation of wide equal-mass massive binaries is
common in metal-free/metal-poor star formation, mainly driven by their large
accretion rates. We expect that the lower gas temperature and accretion rates
in metal-enriched circumstellar discs would lead more often to inward migration
and closer binary separations. We also observe inward migration for smaller
mass Pop III protostars/fragments, leading to the rapid merging of sink
particles and likely the formation of close binary black holes that, however,
reach separations below the resolution of our simulations. We discuss the
implications that Pop III separations and ellipticity may have on the
interpretation that gravitational wave signals from merging intermediate-mass
black holes come from Pop III remnants.
