  A positive cosmological constant $\Lambda >0$ sets an upper limit for the
area of marginally future-trapped surfaces enclosing a black hole (BH). Does
this mean that the mass of the BH cannot increase beyond the corresponding
limit? I analyze some simple spherically symmetric models where regions within
a dynamical horizon keep gaining mass-energy so that eventually the $\Lambda$
limit is surpassed. This shows that the black hole proper transmutes into a
collapsing universe, and no observers will ever reach infinity, which
dematerializes together with the event horizon and the `cosmological horizon'.
The region containing the dynamical horizon cannot be causally influenced by
the vast majority of the spacetime, its past being just a finite portion of the
total, spatially infinite, spacetime. Thereby, a new type of horizon arises,
but now relative to past null infinity: the boundary of the past of all
marginally trapped spheres, which contains in particular one with the maximum
area $4\pi/\Lambda$. The singularity is universal and extends mostly outside
the collapsing matter. The resulting spacetimes models turn out to be
inextendible and globally hyperbolic. It is remarkable that they cannot exist
if $\Lambda$ vanishes. Given the accepted value of $\Lambda$ deduced from
cosmological observations, such ultra-massive objects will need to contain a
substantial portion of the total {\it present} mass of the {\it observable}
Universe.

General Relativity and Quantum Cosmology;High Energy Physics - Theory