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This paper introduces a new paradigm of surface topography transition and its relation to the functional properties of stratified surfaces. These surfaces are generated by various machining processes that create the particular surface texture components. Therefore, these surfaces are also called multi-process or multifunctional surfaces, because each surface texture component plays a different function. Additionally, during the exploitation period, the wear processes occur. These processes cause the phenomenon of topography transition, which changes the surface features and affects their tribological properties. It is important to understand how surface topography features change due to these processes and how they influence performance aspects. It is also important to understand how these changes and properties can be measured, in order to improve the process of quality control and analysis of functional characteristics. Stratified surfaces with three Gaussian components of the height distribution, such as the surface texture of the cylinder liner after use, are analysed. A new paradigm based on the new mathematical model of the Material Probability Curve (MPC) is proposed to describe and predict the surface transitional transformations and their consequences on the functional properties. The results of the analysis of cylinder liner surfaces are presented on the basis of this model. These results show that this new MPC model effectively characterises the surface topography changes and provides tribologically important information. The adjusted R square value in each case showed that the three-Gaussian model of MPC better fit the MPC of that surface texture than the two-Gaussian model of MPC. The average adjusted R2 for the three-Gaussian model was 0.997564, while for the two-Gaussian model it was 0.980234. This means that this value was closer to 1 for the three-Gaussian model and therefore this model was more accurate for describing the MPC. Additionally, it was found that the two-Gaussian model of MPC overstates values (by 50% on average) for the standard deviation in the plateau part than the three-Gaussian model. The two-Gaussian model cannot distinguish the two Gaussian components that are present in the valley region, so it tries to find their average value. On the other hand, the three-Gaussian model of MPC enables us to identify and analyse in detail the specific Gaussian components in each surface texture area. The model can also provide useful information for controlling the machining and wear processes and improving the quality and reliability of the stratified surfaces; as well as describe the surface topography transition and its relation to the functional properties more accurately than the existing two-Gaussian MPC model. [ABSTRACT FROM AUTHOR]