—We investigate distributed channel-aware random access for networks with arbitrary topologies and traffic distributions, where users can receive traffic from or send traffic to different users and different communication links may interfere with others. We consider heterogeneous channels, where the random channel gains of different links may have different distributions. To resolve the network contention in a distributed way, each frame is divided into contention and transmission periods. The contention period is used to resolve conflicts near optimally and to schedule users with better channel states with higher probabilities while assuring fairness among all users. The proposed scheme completely resolves contention of networks with arbitrary topologies and is robust to any channel uncertainty. Besides, it performs close to central schedulers.