Hepatocellular carcinoma (HCC) can be potentially discovered from abdominal computed tomography (CT) studies under varied clinical scenarios, e.g., fully dynamic contrast enhanced (DCE) studies, non-contrast (NC) plus venous phase (VP) abdominal studies, or NC-only studies. We develop a flexible three-dimensional deep algorithm, called hetero-phase volumetric detection (HPVD), that can accept any combination of contrast-phase inputs and with adjustable sensitivity depending on the clinical purpose. We trained HPVD on 771 DCE CT scans to detect HCCs and tested on external 164 positives and 206 controls, respectively. We compare performance against six clinical readers, including two radiologists, two hepato-pancreatico-biliary (HPB) surgeons, and two hepatologists. The area under curve (AUC) of the localization receiver operating characteristic (LROC) for NC-only, NC plus VP, and full DCE CT yielded 0.71, 0.81, 0.89 respectively. At a high sensitivity operating point of 80% on DCE CT, HPVD achieved 97% specificity, which is comparable to measured physician performance. We also demonstrate performance improvements over more typical and less flexible non hetero-phase detectors. Thus, we demonstrate that a single deep learning algorithm can be effectively applied to diverse HCC detection clinical scenarios.