In this paper, we propose a general framework to investigate cooperative non-orthogonal multiple access (NOMA) using two-stage relay selection (TSRS) in spatially random relaying networks. More specifically, we consider both amplify-and-forward (AF) and decode-and-forward (DF) protocols and compare the performance between them. From practical consideration, we adopt a stochastic geometrybased model and assume that the spatial topology of relays is modeled by using homogeneous poisson point process (PPP). Based on such a setting, an effective coverage area of the relays modeled by using homogeneous PPP in cooperative NOMA systems is developed and performance comparison between TSRS and the conventional max-min RS scheme is also presented. According to the locations of the NOMA users, we develop the complete strategies for calculating the effective coverage area of the relays. Furthermore, in the high signal-to-noise ratio regime, asymptotic expressions are provided to show that the outage probability tends to a constant which is only related to the density of homogeneous PPP and the effective coverage area of the relays. For a given outage probability, we reveal the relationship between the shortest and longest radiuses of the effective district of the relays. Finally, Monte Carlo simulations are provided to verify the accuracy of the analytical results.