Highly anisotropic cellulose nanofibrils can solidify liquid water, creating self-supporting structures by incorporating a tiny number of fibrils. These fibrillar hydrogels can contain as much as 99.99 wt% water. The structure and mechanical properties of fibrillar networks have so far not been completely understood, nor how they solidify the bulk water at such low particle concentrations. In this work, the mechanical properties of cellulose fibrillar hydrogels in the dilute regime from a wt% perspective have been studied, and an elastoplastic model describing the network structure and its mechanics is presented. A significant insight from this work is that the ability of the fibrils to solidify water is very dependent on particle stiffness and the number of contact points it can form in the network structure. The comparison between the experimental results and the theoretical model shows that the fibrillar networks in the dilute regime form via a non-stochastic process since the fibrils have the time and freedom to find contact points during network formation by translational and rotational diffusion. The formed, dilute fibrillar network deforms by sliding fibril contacts upon straining the network beyond its elastic limit. Our results also show that before macroscopic failure, the fibril contacts are restored once the load is released. The exceptional properties of this solidified water are exploited to host fluidic channels, allowing directed fluid transportation in water. Finally, the microfluidic channels formed in the hydrogels are tailored by the layer-by-layer technique to be interactive against external stimuli, a characteristic envisioned to be useful in biomedical applications.