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The envisioned Internet of Things (IoT) will involve a massive deployment of objects connected through wireless cells. While commercial solutions are already available, the fundamental limits of such networks in terms of node density, achievable rates or reliability are not known. To address this question, this paper uses a large scale Multiple Access Channel (MAC) to model IoT nodes randomly distributed over the coverage area of a unique base station. The traffic is represented by an information rate spatial density ρ(x). This model, referred to as the Spatial Continuum Multiple Access Channel, is defined as the asymptotic limit of a sequence of discrete MACs. The access capacity region of this channel is defined as the set of achievable information rate spatial densities achievable with vanishing transmission errors and under a sum-power constraint. Simulation results validate the model and show that this fundamental limit theoretically achievable when all nodes transmit simultaneously over an infinite time, may be reached even with a relatively small number of simultaneous transmitters (typically around 20 nodes) which gives credibility to the model. The results also highlight the potential interest of non-orthogonal transmissions for IoT uplink transmissions when compared to an ideal time sharing strategy.