Orientational ordering in monolayers of solid hydrogen is discussed in view of recent experimental findings in NMR studies of ðorthoÞ c -ðparaÞ 12c -hydrogen mixtures on boron nitride substrate reported for ortho-H 2 concentrations 0:35 # c # 0:92 and temperatures 0:14 # T # 1:80 K. Analysis of the temperature-concentration behavior for the observed NMR frequency splitting is given on the basis of a two-dimension ðJ ¼ 1Þ c -ðJ ¼ 0Þ 12c -rotor model for which the fundamental parameters, quadrupolar coupling constant G 0 ¼ 0:50 ^0:03 K and the crystal-field amplitude V 0 ¼ 0:70 ^0:10 K, are derived from experiment. The two distinct para-rotational (PR) short-range ordered structures driven by positive and negative crystalline fields are described in terms of the local alignment and orientation of the polar principal axis. It is shown that they are rather different from the ferromagnetic-type ordering suggested earlier by Harris and Berlinsky as a unique PR structure. The common quadrupolar glass and a new hindered rotor phases found below the 2D site percolation threshold c p ¼ 0:72 are also discussed.