  We study corner contributions to holographic mutual information for
entangling regions composed of a set of disjoint sectors of a single infinite
circle in three-dimensional conformal field theories. In spite of the UV
divergence of holographic mutual information, it exhibits a first order phase
transition. We show that tripartite information is also divergent for disjoint
sectors, which is in contrast with the well-known feature of tripartite
information being finite even when entangling regions share boundaries. We also
verify the locality of corner effects by studying mutual information between
regions separated by a sharp annular region. Possible extensions to higher
dimensions and hyperscaling violating geometries is also considered for
disjoint sectors.
