Numerous geological features that could be evaporitic in origin have been identified on the surface of Titan. Although they seem to be water-ice poor, their main properties -chemical composition, thickness, stratification- are essentially unknown. In this paper, which follows on a previous one focusing on the surface composition (Cordier et al., 2013), we provide some answers to these questions derived from a new model. This model, based on the up-to-date thermodynamic theory known as "PC-SAFT", has been validated with available laboratory measurements and specifically developed for our purpose. 1-D models confirm the possibility of an acetylene and/or butane enriched central layer of evaporitic deposit. The estimated thickness of this acetylene-butane layer could explain the strong RADAR brightness of the evaporites. The 2-D computations indicate an accumulation of poorly soluble species at the deposit's margin. Among these species, HCN or aerosols similar to tholins could play a dominant role. Our model predicts the existence of chemically trimodal "bathtub rings" which is consistent with what it is observed at the south polar lake Ontario Lacus. This work also provides plausible explanations to the lack of evaporites in the south polar region and to the high radar reflectivity of dry lakebeds.