Static coseismic offsets >1 mm are observed up to 7800 km away from the great Sumatra-Andaman earthquake of 26 Dec. 2004 using global GPS network data. We investigate the rupture process based on far-field continuous GPS data. To reduce error in the coseismic offset estimates due to post-seismic deformation in the days following the main shock, we simultaneously fit a model of co- and postseismic offsets for nearby stations SAMP (500 km) and NTUS (900 km). The 3-month cumulative postseismic displacement for station SAMP amounts to 20% of the coseismic displacement, and can be well modeled by velocity-strengthening afterslip. We find that coseismic slip on the northern rupture segment is ∼3 m, which is consistent with seismic estimates. Our best estimate of the moment magnitude is Mw = 9.13 if we take into account the expected increase of the shear modulus with depth (for uniform µ = 30 GPa, the moment-magnitude would only be 8.97). Our geodetic results, and thus our inferred rupture model, are different from a similar study using far-field data of Banerjee et al. (2005). These differences highlight the challenge in earthquake studies on a global scale in terms of the sensitivity of far-field offset estimates to the analysis strategy and reference frame treatment. Our predicted coseismic offsets from this event are at least 1 mm across almost the entire globe. This warrants a reconsideration of how to maintain the global terrestrial reference frame affected by earthquakes of Mw > 9.0.