  It has been long known that in spacetimes with a positive cosmological
constant $\Lambda >0$ the area of spatially stable marginally trapped surfaces
(MTSs) has a finite upper bound given by $4\pi/\Lambda$. In this paper I show
that any such spacetime containing spatially stable MTSs with area approaching
indefinitely that bound acquire universal properties generically. Specifically,
they all possess {\em generalized} `holographic screens' (i.e. marginally
trapped tubes) foliated by MTSs of spherical topology, composed of a dynamical
horizon portion and a timelike membrane portion that meet at a distinguished
round sphere $\bar S$ with constant Gaussian curvature $\mathcal{K} =\Lambda$
-- and thus of maximal area $4\pi/\Lambda$. All future (past) generalized
holographic screens containing $\bar S$ change signature at $\bar S$, and all
of them continue towards the past (future) with non-decreasing (non-increasing)
area of their MTSs. A future (past) singularity obtains. For the future case,
these `ultra-massive spacetimes' (arXiv:2209.14585) may be more powerful than
black holes, as they can overcome the repulsive $\Lambda$-force and render the
spacetime as a collapsing universe without event horizon enclosing those
generalized holographic screens. It is remarkable that these behaviours do not
arise if $\Lambda$ is non-positive. The results have radical implications on
black hole mergers and on very compact objects accreting mass from their
surroundings -- if $\Lambda >0$.
