The contact resistivity is a key parameter to reach high conversion efficiency in solar cells, especially in architectures based on the so-called carrier-selective contacts. The importance of contact resistivity relies on the evaluation of the quality of charge collection from the absorber bulk through adjacent electrodes. The electrode usually consists of a stack of layers entailing complex charge transport processes. This is especially the case of silicon heterojunction (SHJ) contacts. Although it is known that in thin-film silicon, the transport is based on subgap energy states, the mechanisms of charge collection in SHJ systems is not fully understood yet. Here, we analyse the physical mechanisms driving the exchange of charge among SHJ layers with the support of rigorous numerical simulations that reasonably replicate experimental results. We observe a connection between recombination and collection of carriers. Simulation results reveal that charge transport depends on the alignment and the nature of energy states at heterointerfaces. Our results demonstrate that transport based on direct energy transitions is more efficient than transport based on subgap energy states. Particularly, for positive charge collection, energy states associated to dangling bonds support the charge exchange more efficiently than tail states. The conditions for optimal carrier collection rely on the Fermi energy of the layers, in terms of activation energy of doped layers and carrier concentration of transparent conductive oxide. We observe that fill factor (FF) above 86% concurrently with 750-mV open circuit voltage can be attained in SHJ solar cells with ρ_c lower than 45 mΩ·cm² for p-contact and 20 mΩ·cm² for the n-contact. Furthermore, for achieving optimal contact resistivity, we provide engineering guidelines that are valid for a wide range of silicon materials from amorphous to nanocrystalline layers.