A thermodynamic approach describing the precipitation of asphaltene materials from petroleum fluids as a consequence of aggregate break-up is presented. The aggregation equilibrium for asphaltenes and resins is considered along with the bulk-phase equation of state (EOS) to account for the effects of pressure and solvents on the thermodynamic behavior of asphaltene dispersions. Polydispersity of asphaltene aggregates is taken into account. The effect of the resin molecular shape on the size distribution is considered. Relation between the shape factors and elastic constants of the resin shell of the aggregates is given. Precipitation curves for several real crude oil mixtures are calculated and structural characteristics of the aggregates are estimated. Comparison with the experimental data shows that the results are reasonable.