Do black hole horizons always increase? In asymptotically flat spacetimes, the area of a black hole event horizon must always increase, provided the Null Convergence Condition is followed ($R_{\mu\nu}k^{\mu}k^{\nu}\geq0$ for all null vectors $k^{\mu}$) (S.W. Hawking, Gravitational radiation from colliding black holes, Phys. Rev. Lett. 26 (1971) 1344.). This is sometimes called the "second law of black hole thermodynamics".
Does this result also hold for black holes in asymptotically FLRW spacetimes (expanding and/or contracting)? I am mostly trying to find papers on this subject; I have only found this paper by Hawking and Gibbons on black holes in asymptotically de Sitter spacetimes.
 A: If the Hubble parameter H and the dark energy density c²Λ/(8πG) is constant like in the Schwarzschild De Sitter metric then also the horizon will stay constant if the black hole is not fed.
If the dark energy density was time dependend like in some phantom dark energy models then the coordinate radius of the horizon would also expand or shrink with time since the whole metric also depends on Λ.
If only H but not Λ changes like in the FLRW/ΛCDM metric the black hole horizon also stays constant due to the shell-theorem, since the change in H comes from the change in the overall density of all the galaxies around the black hole which are distributed homogenous and isotropely and therefore spherically symmetric, so only Λ and M count.
The last paper you linked is including quantum mechanics by the way, while my comment doesn't.
A: Asked in this generality the answer would have to be no because black holes would   evaporate when left alone, which implies that their horizon eventually decreases.
