The dedicated satellite gravity missions CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), and Gravity field and steady-state Ocean Circulation Explorer (GOCE) and their recent and expected Global Geopotential Models (GGMs) present new opportunities for the determination of gravity-related heights. Global Positioning System (GPS), the recent GGMs, and reference value W-0 are used to study the construction of different height systems and verify high-degree global geopotential models. This approach matches well with all theoretical basics of height systems. The presented numerical strategy is independent of height anomaly and geoid undulation computation. Using the International Terrestrial Reference Frame (ITRF) coordinates at 47 GPS stations of the Turkish National Vertical Control Network (TNVCN), the gravity potential values are computed based on new-generation GGMs. The computed gravity potentials are converted into different height systems. A global mean sea level represented by a geoid potential has been taken as reference for the heights. The GGM-derived geopotential numbers, Helmert orthometric, and Molodensky normal heights at the GPS stations are compared against the results from precise leveling. The numerical application demonstrates that three types of gravity-related heights can be determined with a similar accuracy level (+/- 12 cm). When long-term deformations such as tectonic activity and possible land subsidence/uplift eFF ects on the heights of benchmarks of the TNVCN are taken into account, the obtained results are significant, and also, under the light of the dedicated satellite gravity missions, high-resolution GGMs such as EGM2008 have an important potential for the realization of a unified height system. The experimental study shows a datum bias of 38 +/- 2 cm between the TNVCN datum and the global datum.