An interaction site-based model of two-dimensional alcohols is proposed as a follow up of the recent SSMB site-site model for 2D water [J. Mol. Liq. 386 (2023 122475 ]. Computer simulation studies indicate that the model exhibits hbond-type clustering based on the same charge order feature observed in real alcohols. Hence, the equivalent of 2D mono-ols ranging from methanol to octanol were studied for their clustering properties, focusing on how the micro-structure aects the shape of the site-site pair correlation functions and structure factors, as well as the combination of the latter into the radiation scattering intensities. The major nding is the apparent contradiction between the existence of large pre-peaks in the structure factors, usually associated to the existence of clusters, and the exponential decay of the cluster distribution indicating the absence of specic clusters, contrary to the 3D case. This is resolved by realizing that the pair correlation function is an observable of the local density uctuations, hence the pre-peak witnesses uctuations around clustering tendencies, which are the result of charge ordering of the polar groups, and visible in the snapshots. The scattering pre-peak witnesses only uctuations due to charge ordering, and not the clusters themselves, underlining the fact that these are labile entities. The study highlights how charge order through atomic sites is a universal feature behind the micro-structure of organized liquids, and, in the particular case of 2D liquids, a more realistic alternative to orientation based models such as the Mercedes-Benz model, for instance.