The ex novo lipid accumulation process in the yeast Yarrowia lipolytica was systematically studied in the current investigation. Various fatty materials of plant (i.e. olive, sunflower, palm, linseed oils) or animal (i.e. cod liver oil, beef tallow) origin, the fatty acid (FA) composition of which resembled in several cases to the one of important low- or negative-cost hydrophobic resources (i.e. stickwaters, fat-rich wastes from meat-processing facilities, used-cooked oils, etc) were employed as substrates and a detailed mathematical model which included description of substrate fat hydrolysis, biomass and reserve lipid formation and cellular lipid turnover was developed. The kinetic parameter values were calculated by fitting the model on experimental data and used to estimate the ability of the yeast to grow on the various substrate fats and modify their FA composition. With few exceptions the substrate fat was efficiently converted into yeast cells (biomass) rich in lipids consisting mainly of neutral lipids (often >90% on the total lipids), indicating, therefore the potential of the yeast Y. lipolytica as cell factory amenable to ferment several types of low-cost fatty materials. The contribution of each substrate fatty acid (FA) to the synthesis of fat free biomass varied according to the theoretical FA uptake rate and typically was higher for palmitic, oleic and linoleic acid than the remaining FAs. Eicosapentaenoic and docosohexaenoic acids, typically found in several stickwaters or crude fish oils, were also rapidly taken up when cod liver oil was used as substrate. Respectively, the contribution of the substrate FAs to the synthesis of storage lipid was more important for linoleic and palmitic acids. Higher proportions of unsaturated FAs were esterified in phospholipid fraction. Upon exhaustion of the substrate fat, storage lipid degradation occurred. Unsaturated (primarily monounsaturated) FA uptake rates were higher than those of saturated FAs and therefore storage lipid was enriched in saturated FAs during lipid turnover. Storage lipid degradation can be successfully repressed (or even its biosynthesis can be restored) with the addition of a carbon source (e.g. glycerol, glucose, olive oil) in the culture medium during lipid degradation. We concluded that the mathematical approach proposed in this paper can constitute an effective tool for better understanding several key biochemical events, including substrate fat modification, during growth of Y. lipolytica on common oils. Through the proposed approach, low cost fatty materials such as stickwaters, fat-rich wastewaters from meat-processing facilities, used-cooked oils, soap stocks, stearins, etc., can be efficiently converted in higher-value cellular lipids by Y. lipolytica through completely eco-friendly and green processes.