Recently, the idea of opportunistic routing (OR) has been widely explored to cope with the unreliable transmissions by exploiting the broadcast nature and spatial diversity of the wireless medium in order to improve the performance of wireless sensor networks. However, there are few theoretical analyses on the maximum throughput of OR WSNs. This paper is the first attempt to conduct a theoretical analysis on aggregate throughput capacity of OR in multihop many-to-one WSNs with consideration for lossy link and transmission fairness. By capturing the key characteristics of forwarding candidate set in OR networks, we propose the cumulative delivery transmission model. Then we introduce the concept of concurrent schedulable set to represent the constraints imposed by the transmission conflicts of OR, and formulate the optimal aggregate throughput problem as a maximum concurrent flow linear programming problem. Simulation results demonstrate that the OR design derived from our analysis model often yields noticeably better throughput than traditional unicast routing protocols and the OR design derived from existing analysis model under a range of scenarios.