Triacylglycerols (TAGs) are biologically important molecules which form crystalline nanoplatelets (CNPs) and, ultimately, fat crystal networks in edible oils. Characterizing the self-assembled hierarchies of these networks is important to understanding their functionality and oil binding capacity. We have modelled CNPs in multicomponent oils and studied their aggregation. The oil comprises (a) a liquid component, and (b) components which phase separately on a nano-scale (nano-phase separation) to coat the surfaces of the CNPs impenetrably, either isotropically or anisotropically, with either liquid-like coatings or crystallites, forming a coating of thickness ?. We modelled three cases: (i) liquid?liquid nano-phase separation, (ii) solid?liquid nano-phase separation, with CNPs coated isotropically, and (iii) CNPs coated anisotropically. The models were applied to mixes of tristearin and triolein with fully hydrogenated canola oil, shea butter with high oleic sunflower oil, and cotton seed oil. We performed Monte Carlo simulations, computed structure functions and concluded: (1) three regimes arose: (a) thin coating regime, Δ < 0.0701 u (b) transition regime, 0.0701 u ≤ Δ ≤ 0.0916 u and (c) thick coating regime, Δ > 0.0916 u. (arbitrary units, u) (2) The thin coating regime exhibits 1D TAGwoods, which aggregate, via DLCA/RLCA, into fractal structures which are uniformly distributed in space. (3) In the thick coating regime, for an isotropic coating, TAGwoods are not formed and coated CNPs will not aggregate but will be uniformly distributed in space. For anisotropic coating, TAGwoods can be formed and might form 1D strings but will not form DLCA/RLCA clusters. (4) The regimes are, approximately: thin coating, 0 < Δ < 7.0 nm transition regime, 7.0 < Δ < 9.2 nm and thick coating, Δ > 9.2 nm (5) The minimum minority TAG concentration required to undergo nano-phase separation is, approximately, 0.29% (thin coatings) and 0.94% (thick coatings). Minority components can have substantial effects upon aggregation for concentrations less than 1%.