Carrier-selective passivating contacts have been demonstrated to be crucial to reach the practical efficiency limit of single junction, crystalline silicon (c-Si) based solar cells. Yet, the electrical transport losses affecting the collection of photogenerated carriers remain to be addressed. To this aim, different methodologies and characterization techniques are currently used. In this contribution, we propose the concept of shell as a new terminology to describe carrier-selective passivating contacts. Then, we present a novel characterization methodology using transfer length method (TLM) measurement under variable illumination to investigate the charge-carrier transport in amorphous/crystalline silicon heterojunction (SHJ) n-type contact stacks. We use technology computer-aided design simulation to model a TLM structure and to identify the physical phenomena and the key parameters affecting the contact resistivity (ρc) and the charge carrier accumulation of such contact stacks. Then, the simulation results are compared with experimental data by performing variable-illumination TLM measurements of actual SHJ n-type contact stacks. Specifically, we demonstrate that illumination has a strong impact on the measured ρc value, highlighting the importance of measuring ρc under maximum power point conditions for a relevant characterization of solar cell transport losses. In addition, we investigate the dependence of ρc to a change in the injected carrier density within the c-Si bulk to compare the illumination responses of different SHJ n-type contact stacks. In the quest for maximal efficiency, this method may insightfully complete other characterization techniques to further understand and study the electrical transport in solar cells.