Modules composed of parallel-connected cells are employed as the building block of battery packs in order to achieve an increase in output current and system reliability. Given that the current distribution among cells is not known beforehand, standard electrochemical models are not well conditioned for the simulation of parallel-connected cells. Additionally, interconnection and contact resistances, along with cell-to-cell variations, play a major role in the module voltage and current distribution. In this contribution, the physically motivated discrete transmission line cell model is employed, and its circuit formulation is exploited for the direct calculation of the instantaneous equivalent voltage and resistance of each cell. This, in turn, allows for an efficient computation of module voltage and current distribution at each timestep, regardless of the values of interconnection and contact resistances or the number of cells connected in parallel. The presented approach is validated against an experimental 4-parallel dataset in which the interconnection resistance, ambient temperature, and the presence of an aged cell are considered as control variables. Accurate results are provided for both the module voltage and current distribution with a single set of constant parameters for the considered scenarios. Furthermore, the proposed simulation approach allows evaluating the effect of different factors independently: the interconnection resistance causes a significant drop in module voltage and an increasingly heterogeneous current distribution, whereas the presence and position of an aged cell affect the current distribution to a greater extent than the module voltage, thus illustrating self-balancing behavior. In conclusion, module behavior is shown to be qualitatively and quantitatively different from that of an equivalent lumped cell, but can be assessed efficiently within the presented framework for the development of advanced estimation and management strategies.