  In this paper we consider the maximal volume and the action, which are
conjectured to be gravity duals of the complexity, in the black hole geometries
with end of the world branes. These geometries are duals of boundary states in
CFTs which have small real space entanglement. When we raise the black hole
temperature while keeping the cutoff radius, black hole horizons or end of the
world branes come in contact with the cutoff surface. In this limit,
holographic entanglement entropy reduces to 0. We studied the behavior of the
volume and the action. We found that the volume reduces to 0 in this limit. The
behavior of the action depends on their regularization. We study the
implication of these results to the reference state of the holographic
complexity both in the complexity = volume or the complexity = action
conjectures.
