  We investigate the thermodynamic phase behaviour of rotating and slowly
accelerating AdS black holes. While we find some similarities with the
non-rotating charged counterparts, such as the peculiar phenomena of "snapping
swallow tails" we also find subtle but significant distinctions that can be
attributed to a qualitatively modified parameter space of the solution.
Consequently the zeroth order phase transition now occurs over a range of
pressures, mini-entropic black holes no longer exist in the regime of slow
acceleration, and the "no black hole region" emerges continuously---from a zero
temperature extremal black hole. The formerly equal transition pressure now
experiences a fine splitting, as the emergence of a no black hole region and
the zeroth-order phase transition appear at different pressures, different also
from the termination pressure of the first order phase transition. This has the
further effect of admitting reentrant phase transitions that can be achieved in
two ways, either by varying the temperature at fixed pressure or varying the
pressure at fixed temperature.
