  Two-dimensional (2D) KPZ growth is usually investigated on substrates of
lateral sizes $L_x=L_y$, so that $L_x$ and the correlation length ($\xi$) are
the only relevant lengths determining the scaling behavior. However, in
cylindrical geometry, as well as in flat rectangular substrates $L_x \neq L_y$
and, thus, the surfaces can become correlated in a single direction, when $\xi
\sim L_x \ll L_y$. From extensive simulations of several KPZ models, we
demonstrate that this yields a dimensional crossover in their dynamics, with
the roughness scaling as $W \sim t^{\beta_{\text{2D}}}$ for $t \ll t_c$ and $W
\sim t^{\beta_{\text{1D}}}$ for $t \gg t_c$, where $t_c \sim
L_x^{1/z_{2\text{D}}}$. The height distributions (HDs) also cross over from the
2D flat [cylindrical] HD to the asymptotic Tracy-Widom GOE [GUE] distribution.
Moreover, 2D-to-1D crossovers are found also in the asymptotic growth velocity
and in the steady state regime of flat systems, where a family of universal HDs
exists, interpolating between the 2D and 1D ones as $L_y/L_x$ increases.
Importantly, the crossover scalings are fully determined and indicate a
possible way to solve 2D KPZ models.
