  The phase diagram of a para-H2 monolayer absorbed on a experimentally
syntetized amorphous carbon sheet was calculated using a diffusion Monte Carlo
technique. We found that the ground state of that system changed drastically
from a perfectly flat substrate to a situation in which the carbon atoms were
allowed a certain degree of disorder in the $z$ direction. In the first case,
at zero pressure we have a glass of density 0.056 $\pm$ 0.003 \AA$^{-2}$ in
equilibrium with an incommensurate solid of 0.068 $\pm$ 0.002 \AA$^{-2}$. At
the equilibrium density, the glass was found to have a tiny, but non-negligible
superfluid faction of less than 1 \% (0.44 $\pm$ 0.05 \%). In the
$z$-disordered substrate, we observe a significant enhancement of the
superfluid fraction in the glass phase as well as a smaller but not zero value
in the incommensurate crystal.
