The cooperative medium access control (CoopMAC) protocol in the presence of randomly-distributed nodes and shadowing is considered. The nodes are assumed to be distributed according to a homogeneous two-dimensional Poisson point process. A new approach is proposed for helper selection and throughput performance analysis which depends on the shadowing parameters as well as the distribution of helpers. In the proposed protocol, the potential helpers are divided into several tiers based on their distances from the source and destination in a way that the lower the tier index, the higher its priority. When there are several helpers of the same tier, the helper that is less affected by shadowing is chosen for cooperation. Upper and lower bounds are derived for the average cooperative throughput of the proposed CoopMAC protocol. It is observed that the proposed scheme readily outperforms the conventional CoopMAC protocol in having larger average throughput. It is also seen that the cooperative throughput of the proposed scheme approaches the upper bound when the density of nodes increases.