This paper investigates the precision of the estimation of geophysical fluid load deformation computed from GRACE space gravity, GPS vertical displacement and geophysical fluids models [Global Circulation Models (GCMs) for ocean, atmosphere and hydrology], using the three-cornered hat method. This method allows the estimation of the variance of the errors of each technique, when the same quantity is monitored by three instruments with independent errors. Applied on a network of stations, several points of view can be considered: the technique level (in order to determine the error of each technique: GRACE, GPS and GCMs), the solution level (allowing to compare the precision of the same technique when different strategies/models are used), and the station level (in order to emphasize local anomalies and geographical patterns). In particular, our results show a precision of the loading vertical displacement at the level of 1 mm when using GRACE or the fluid models, and of 2 mm using GPS. We do not find significant differences between the precision of different solutions of the same techniques, even when there are strong differences in the data processing.