  We characterize limit fluctuations of height functions of the totally
asymmetric simple exclusion processes with open boundaries at the co-existence
line under the stationary measures. The limit behavior of the height functions
at the co-existence line was known to be exotic in the sense that the
first-order limit theorem (when divided by $n$) has a random limit. Here, we
show that with a random centering and then divided by $\sqrt n$, the
second-order limit of the height functions is a (random) mixture of two
independent Brownian motions.
