Accurate assessment of 3D models of patient-specific anatomy of the liver, including underlying hepatic and biliary tree, is critical for preparation and safe execution of complex liver resections, especially due to high variability of biliary and hepatic artery anatomies. Dynamic MRI with hepatospecific contrast agents is currently the only type of diagnostic imaging that provides all anatomical information required for generation of such a model, yet there is no information in the literature on how the complete 3D model can be generated automatically. In this work, a new automated segmentation workflow for extraction of patient-specific 3D model of the liver, hepatovascular and biliary anatomy from a single multiphase MRI acquisition is developed and quantitatively evaluated. The workflow incorporates course 4D k-means clustering estimation and geodesic active contour refinement of the liver boundary, based on organ's characteristic uptake of gadolinium contrast agents overtime. Subsequently, hepatic vasculature and biliary ducts segmentations are performed using multiscale vesselness filters. The algorithm was evaluated using 15 test datasets of patients with liver malignancies of various histopathological types. It showed good correlation with expert manual segmentation, resulting in an average of 1.76 ± 2.44 mm Hausdorff distance for the liver boundary, and 0.58 ± 0.72 and 1.16 ± 1.98 mm between centrelines of biliary ducts and liver veins, respectively. A workflow for automatic segmentation of the liver, hepatic vasculature and biliary anatomy from a single diagnostic MRI acquisition was developed. This enables automated extraction of 3D models of patient-specific liver anatomy, and may facilitating better perception of organ's anatomy during preparation and execution of liver surgeries. Additionally, it may help to reduce the incidence of intraoperative biliary duct damage due to an unanticipated variation in the anatomy.