  We prove local convergence results for the uniformly random, labelled or
unlabelled, graphs from subcritical families. As an example special case, we
prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We
introduce a compactification of the space of countable (connected) rooted
graphs, and use it to generalise the notion of Benjamini-Schramm convergence in
order to allow for vertices of infinite degree in the limit object.
