  Simulations of restricted solid-on-solid growth models are used to build the
width-distributions of d=2-5 dimensional KPZ interfaces. We find that the
universal scaling function associated with the steady-state width-distribution
changes smoothly as d is increased, thus strongly suggesting that d=4 is not an
upper critical dimension for the KPZ equation. The dimensional trends observed
in the scaling functions indicate that the upper critical dimension is at
infinity.
