  We study the Page curve and the island rule for black holes evaporating into
gravitating baths, with an eye towards establishing a connection with the
ER=EPR proposal. We consider several models of two entangled 2d black holes in
Jackiw-Teitelboim (JT) gravity with negative cosmological constant. The first,
"doubled PSSY," model is one in which the black holes have end-of-the-world
(ETW) branes with a flavour degree of freedom. We study highly entangled states
of this flavour degree of freedom and find an entanglement-induced
Hawking-Page-like transition from a geometry with two disconnected black holes
to one with a pair of black holes connected by a wormhole, thus realising the
ER = EPR proposal. The second model is a dynamical one in which the ETW branes
do not have internal degrees of freedom but the JT gravity is coupled to a 2d
CFT, and we entangle the black holes by coupling the two CFTs at the $AdS$
boundary and evolving for a long time. We study the entanglement entropy
between the two black holes and find that the story is substantially similar to
that with a non-gravitating thermal bath. In the third model, we couple the two
ends of a two-sided eternal black hole and evolve for a long time. Finally, we
discuss the possibility of a Hawking-Page-like transition induced by real-time
evolution that realises the ER = EPR proposal in this dynamical setting.
