Growing thin, nanostructured layers on metallic surfaces is an attractive, new approach to create superhydrophilic coatings on heat exchangers that enhance spray cooling heat transfer. This paper presents results of an experimental study of enhanced droplet spreading on zinc oxide, nanostructured surfaces of this type that were thermally grown on copper substrates. The spreading rate data obtained from experimental high speed videos was used to develop a model specifically for this type of ultrathin, nanoporous layer. This investigation differs from previous related studies of droplet spreading on porous surfaces, which have generally considered either ordered, thin, moderately permeable layers, or thicker, microporous layers. Our layers are both very thin and have nanoscale porosity, making them low-permeability layers that exhibit strong wicking. An added benefit is that the thermally grown, stochastic nature of our surfaces make manufacturing easily scalable and particularly attractive for spray-cooled heat exchanger applications. The model presented here can predict the spreading rate for the wetted footprint of a deposited water droplet over two spreading stages: an early synchronous spreading stage, followed by hemispreading. The comparison of experimental data and model predictions confirms the presence of these two specific spreading stages. The model defines the transition conditions between synchronous and hemispreading regimes based on the change in spreading mechanisms, and we demonstrate that the model predictions of spreading rate are in good agreement with the experimental determinations of droplet footprint variation with time. The results indicate that the early synchronous spreading regime is characterized by flow in the porous layer that is primarily localized near the upper droplet contact line. The potential use of these experimental findings and model for optimizing superhydrophilic, nanostructured surface coatings is also discussed, as it pertains to the surface's ability to enhance water vaporization processes.