We present the results of time-space analysis of synthetic catalogs, generated using a quasi-static discrete fault model that is governed by rate- and state-dependent friction. These analyses reveal that increase in the postmain shock earthquake production rate occurs over an area surrounding the main shock rupture with dimensions that are several times larger than the main shock dimensions. We show that the increase in seismicity rate far from the main shock (where the static stress changes imposed by the main shock were small) is a consequence of multiple stress transfers and that the very distant aftershocks are not directly triggered by the main shock but that instead they are aftershocks of previous aftershocks. Snapshots of the fault state at progressive times prior to each main shock show that the regions which accelerated toward failure covered areas that were much larger than the final size of the main shock ruptures. As a result, as time approached the main shock time, the seismicity rate in these regions increased while the B value of the earthquake size distribution decreased. It has been previously suggested that remote seismicity rate increase could be triggered by the passage of seismic waves. Remote triggering in a quasi-static model indicates that it is not necessary to invoke such a dynamic effect in order to explain distant aftershocks.