Fine-scale anatomical structures in the heart may play an important role in sustaining cardiac arrhythmias. However, the extent of this role and how it may differ between species are not fully understood. In this study we used computational modelling to assess the impact of anatomy upon arrhythmia maintenance in the rabbit ventricles. Specifically, we quantified the dynamics of excitation wavefronts during episodes of simulated tachyarrhythmias and fibrillatory arrhythmias, defined as being respectively characterised by relatively low and high spatio-temporal disorganisation.Two computational models were used: a highly anatomically detailed MR-derived rabbit ventricular model (representing vasculature, endocardial structures) and a simplified equivalent model, constructed from the same MR-data but lacking such fine-scale anatomical features. During tachyarrhythmias, anatomically complex and simplified models showed very similar dynamics; however, during fibrillatory arrhythmias, as activation wavelength decreased, the presence of fine-scale anatomical details appeared to marginally increase disorganisation of wavefronts during arrhythmias in the complex model. Although a small amount of clustering of reentrant rotor centres (filaments) around endocardial structures was witnessed in follow-up analysis (which slightly increased during fibrillation as rotor size decreased), this was significantly less than previously reported in large animals. Importantly, no anchoring of reentrant rotors was visibly identifiable in arrhythmia movies. These differences between tachy- and fibrillatory arrhythmias suggest that the relative size of reentrant rotors with respect to anatomical obstacles governs the influence of fine-scale anatomy in the maintenance of ventricular arrhythmias in the rabbit. In conclusion, our simulations suggest that fine-scale anatomical features play little apparent role in the maintenance of tachyarrhythmias in the rabbit ventricles and, contrary to experimental reports in larger animals, appear to play only a minor role in the maintenance of fibrillatory arrhythmias. These findings also have important implications in optimising the level of detail required in anatomical computational meshes frequently used in arrhythmia investigations.