  We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang
(KPZ) universality class on substrates that expand laterally at a constant rate
by duplication of columns. Despite the null global curvature, we show that all
investigated models have asymptotic height distributions and spatial
covariances in agreement with those expected for the KPZ subclass for curved
surfaces. In $1+1$ dimensions, the height distribution and covariance are given
by the GUE Tracy-Widom distribution and the Airy$_2$ process, instead of the
GOE and Airy$_1$ foreseen for flat interfaces. These results imply that, when
the KPZ class splits into the curved and flat subclasses, as conventionally
considered, the expanding substrate may play a role equivalent to, or perhaps
more important than the global curvature. Moreover, the translational
invariance of the interfaces evolving on growing domains allowed us to
accurately determine, in $2+1$ dimensions, the analogue of the GUE Tracy-Widom
distribution for height distribution and that of the Airy$_2$ process for
spatial covariance. Temporal covariance is also calculated and shown to be
universal in each dimension and in each of the two subclasses. A logarithmic
correction associated to the duplication of column is observed and
theoretically elucidated. Finally, crossover between regimes with fixed-size
and enlarging substrates is also investigated.
