  The experimental realization of a thin layer of spin-polarized hydrogen
adsorbed on top of the surface of superfluid 4He provides one of the best
examples of a stable nearly two-dimensional quantum Bose gas. We report a
theoretical study of this system using quantum Monte Carlo methods in the limit
of zero temperature. Using the full Hamiltonian of the system, composed of a
superfluid 4He slab and the adsorbed hydrogen layer, we calculate the main
properties of its ground state using accurate models for the pair interatomic
potentials. Comparing the results for the layer with the ones obtained for a
strictly two-dimensional (2D) setup, we analyze the departure from the 2D
character when the density increases. Only when the coverage is rather small
the use of a purely 2D model is justified. The condensate fraction of the layer
is significantly larger than in 2D at the same surface density, being as large
as $60\%$ at the largest coverage studied.
