  We study numerically the influence of the substrate (boundary conditions) on
the finite--size scaling properties of the superfluid density $\rho_s$ in
superfluid films of thickness $H$ within the XY model employing the Monte Carlo
method. Our results suggest that the jump $\rho_s H/T_c$ at the
Kosterlitz--Thouless transition temperature $T_c$ depends on the boundary
conditions.
