Wireless energy harvesting has emerged as an efficient solution to prolong the lifetime of wireless networks composed of energy-constrained nodes. In this paper, we consider a multipoint-to-multipoint relay network, where multiple source nodes communicate with their respective destination nodes via intermediate energy-constrained decode-and-forward (DF) relay. The performance of two different transmission modes, namely, delay tolerant and delay nontolerant, is studied. Based on power-splitting relaying protocol (PSR), optimal energy harvesting and distribution schemes for both transmission modes are provided. In addition, for more realistic and practical analysis, we consider a nonlinear energy conversion model for energy harvesting at the relay node. Our numerical results provide useful insights into different system parameters of a nonlinear energy harvesting-based multipair DF relay network.