This paper aims to provide a precise transformation model for the geoid heights between earth geopotential models and regional vertical datum in geodetic applications. With this purpose, Earth Gravitational Model 2008 (EGM08), which is ultra-high-resolution geopotential model, that is complete spherical harmonic degree and order 2190 is considered and fitted to the local vertical datum in three local test areas in west and south of Turkey. The observations at GPS/leveling benchmarks were used for fitting the EGM08 to the local height reference surface and a couple of mathematical methods were evaluated, namely similarity transformation model (STM), polynomial regression model (PRM), least squares collocation (LSC), spline interpolation model (SIM). They are commonly used for corrector surface fitting approaches in height datum studies. Their performances were assessed depending on the statistics at test benchmarks. The results show that fitting of the differences between the GPS/leveling, EGM08-derived geoid heights with LSC, and SIM supplies more accurate solutions than STM and PRM. The accuracies of the achieved models (improved from EGM08 global model) are tested in the several GPS/leveling benchmarks throughout Turkey; the external model accuracy has been estimated as +/- 4-5 cm. In this aspect, this study will provide benefits as both representing the performance of EGM08 model in given local areas and clarifying the modeling performances of the applied transformation approaches for fitting of EGM08 geoid models to GPS/leveling defined vertical datum.