Hydrostatic and hydro-mechanical transmissions (HSTs and HMTs, respectively) are commonly used in off-highway vehicles. While both transmission technologies can provide continuously variable torque or speed ratios, they suffer from poor efficiencies and limited operating ranges. Electric variable transmissions (EVTs), in contrast, offer complementary strengths via higher efficiencies at low forward and reverse speeds, full torque from zero to full power, and increased control capabilities. While HST, HMT, and EVT powertrain architectures are not novel, the authors are not aware of work integrating these technologies into hydro-electro-mechanical (HEMT) transmission architectures. Thus, this research aimed to develop a physical modeling methodology to explore different power-split transmission technologies using hydraulic, electrical, and mechanical pathways to understand how the complementary nature of the technologies could be used for overall power transmission performance. Steady-state modeling was performed using the Modelica® (Modelica Association) modeling language in the Dymola (Dassault Systems®) integrated development environment. Overall efficiency vs. output speed was presented for HMT, EMT, and HEMT input-coupled architectures, including circulating power considerations. This research extends the state-of-the-art of off-road powertrain technologies by providing the literature an exemplar modeling of HEMT coupling techniques, system integration, and power flow architectures in Modelica® modeling language.