We show that the local limit of unicellular maps whose genus is proportional to the number of edges is a supercritical geometric Galton-Watson tree conditioned to survive. The proof relies on enumeration results obtained via the recent bijection given by the second author together with Feray and Fusy.
"The local limit of unicellular maps in high genus." Electron. Commun. Probab. 18 1 - 8, 2013. https://doi.org/10.1214/ECP.v18-3037