A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $p_c$ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $p>p_c$ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.
Itai Benjamini. Oded Schramm. "Percolation Beyond $Z^d$, Many Questions And a Few Answers." Electron. Commun. Probab. 1 71 - 82, 1996. https://doi.org/10.1214/ECP.v1-978