  Motivated by the earlier results, we study theoretically and numerically the
asymptotics and the monodromy of the quasi-exactly solvable part of the
spectrum of the quasi-exactly solvable quartic introduced by C.~M.~Bender and
S.~Boettcher. In particular, we formulate a conjecture on the coincidence of
the asymptotic shape of the configuration of the branching points of the latter
quartic with the asymptotic shape of zeros of the Yablonskii-Vorob'ev
polynomials recently described and present its (conjectural) alternative
description. Further we present a numerical study of the spectral monodromy for
the os- cillator in question.
