We extend existing branching models for earthquake occurrences by incorporating potentially important estimates of tectonic deformation and by allowing the parameters in the models to vary across different tectonic regimes. We partition the Earth’s surface into five regimes: trenches (including subduction zones and oceanic convergent boundaries and earthquakes in outer rise or overriding plate); fast spreading ridges and oceanic transforms; slow spreading ridges and transforms; active continental zones, and plate interiors (everything not included in the previous categories). Our purpose is to specialize the models to give them the greatest possible predictive power for use in earthquake forecasts. We expected the parameters of the branching models to be significantly different in the various tectonic regimes, because earlier studies (Bird and Kagan in Bull Seismol Soc Am 94(6):2380–2399, 2004) found that the magnitude limits and other parameters differed between similar categories. We compiled subsets of the CMT and PDE earthquake catalogs corresponding to each tectonic regime, and optimized the parameters for each, and for the whole Earth, using a maximum likelihood procedure. We also analyzed branching models for California and Nevada using regional catalogs. Our estimates of parameters that can be compared to those of other models were consistent with published results. Examples include the proportion of triggered earthquakes and the exponent describing the temporal decay of triggered earthquakes. We also estimated epicentral location uncertainty and rupture zone size and our results are consistent with independent estimates. Contrary to our expectation, we found no dramatic differences in the branching parameters for the various tectonic regimes. We did find some modest differences between regimes that were robust under changes in earthquake catalog and lower magnitude threshold. Subduction zones have the highest earthquake rates, the largest upper magnitude limit, and the highest proportion of triggered events. Fast spreading ridges have the smallest upper magnitude limit and the lowest proportion of triggered events. The statistical significance of these variations cannot be assessed until methods are developed for estimating confidence limits reliably. Some results apparently depend on arbitrary decisions adopted in the analysis. For example, the proportion of triggered events decreases as the lower magnitude limit is increased, possibly because our procedure for assigning independence probability favors larger earthquakes. In some tests we censored earthquakes occurring near and just after a previous event, to account for the fact that most such earthquakes will be missing from the catalog. Fortunately the branching model parameters were hardly affected, suggesting that the inability to measure immediate aftershocks does not cause a serious estimation bias. We compare our branching model with the ETAS model and discuss the differences in the models parametrization and the results of earthquake catalogs analysis.