Unsupervised/self-supervised graph representation learning is critical for downstream node- and graph-level classification tasks. Global structure of graphs helps discriminating representations and existing methods mainly utilize the global structure by imposing additional supervisions. However, their global semantics are usually invariant for all nodes/graphs and they fail to explicitly embed the global semantics to enrich the representations. In this paper, we propose Omni-Granular Ego-Semantic Propagation for Self-Supervised Graph Representation Learning (OEPG). Specifically, we introduce instance-adaptive global-aware ego-semantic descriptors, leveraging the first- and second-order feature differences between each node/graph and hierarchical global clusters of the entire graph dataset. The descriptors can be explicitly integrated into local graph convolution as new neighbor nodes. Besides, we design an omni-granular normalization on the whole scales and hierarchies of the ego-semantic to assign attentional weight to each descriptor from an omni-granular perspective. Specialized pretext tasks and cross-iteration momentum update are further developed for local-global mutual adaptation. In downstream tasks, OEPG consistently achieves the best performance with a 2%～6% accuracy gain on multiple datasets cross scales and domains. Notably, OEPG also generalizes to quantity- and topology-imbalance scenarios.