We report NMR studies of the orientational ordering of ortho-H-2 molec
ules in 12-layer films physisorbed on hexagonal boron nitride. Tile ph
ase diagram for the ordering has been explored for ortho-H-2 concentra
tion 0.23 < X < 0.72 and for temperatures 0.05 < T < 10K. For high ort
ho concentrations we observe a two-component NMR line shape with a bro
ad central gaussian line (similar to 60 kHz) and a broad outer wing st
ructure (similar to 240 kHz), corresponding to an incompletely orienta
tionally ordered component. The broad component closely resembles the
shapes expected for a quadrupolar glass for this fraction of the molec
ules. The most unusal feature occurs at low concentrations, X < 0.40,
for which we observe a double wing structure, an inner pair with a sep
aration similar to 240 kKz, and an outer pair at similar to 400 kHz. T
he latter are attributed to fully ordered molecules in the first two l
ayers near substrate.