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Building on the work of K. Mann and K. Rafi, we analyze the large scalegeometry of big mapping class groups of surfaces with a unique maximal end. Weobtain a complete characterization of those that are globally CB, which doesnot require the tameness condition. We prove that, for surfaces with a uniquemaximal end, any locally CB big mapping class group is CB generated, and wegive an explicit criterion for determining which big mapping class groups areCB generated. Finally, we give an example of a non-tame surface whose mappingclass group is CB generated but is not globally CB.

On the large scale geometry of big mapping class groups of surfaces with a unique maximal end