  This Letter reports on how the interfaces in the (1+1)-dimensional
Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition
from the flat, growing regime to the stationary one. Simulations of the
polynuclear growth model and experiments on turbulent liquid crystal reveal
universal functions of the KPZ class governing this transition, which connect
the distribution and correlation functions for the growing and stationary
regimes. This in particular shows how interfaces realized in experiments and
simulations actually approach the stationary regime, which is never attained
unless a stationary interface is artificially given as an initial condition.
