  We consider the causal structure of generalized uncharged McVittie spacetimes
with increasing central mass $m (t)$ and positive Hubble factor $H (t)$. Under
physically reasonable conditions, namely, a big bang singularity in the past, a
positive cosmological constant and an upper limit to the central mass, we prove
that the patch of the spacetime described by the cosmological time and areal
radius coordinates is always geodesically incomplete, which implies the
presence of event horizons in the spacetime. We also show that, depending on
the asymptotic behavior of the $m$ and $H$ functions, the generalized McVittie
spacetime can have a single black hole, a black-hole/white-hole pair or,
differently from classic fixed-mass McVittie, a single white hole. A simple
criterion is given to distinguish the different causal structures.
