  We study the large-scale geometry of mapping class groups of surfaces of
infinite type, using the framework of Rosendal for coarse geometry of non
locally compact groups. We give a complete classification of those surfaces
whose mapping class groups have local coarse boundedness (the analog of local
compactness). When the end space of the surface is countable or tame, we also
give a classification of those surface where there exists a coarsely bounded
generating set (the analog of finite or compact generation, giving the group a
well-defined quasi-isometry type) and those surfaces with mapping class groups
of bounded diameter (the analog of compactness).
