In this article, we find the complete list of all contact structures (up to
isotopy) on closed three-manifolds which are supported by an open book
decomposition having planar pages with three (but not less) boundary
components. We distinguish them by computing their first Chern classes and
three dimensional invariants (whenever possible). Among these contact
structures we also distinguish tight ones from those which are overtwisted.Comment: 35 pages, 19 figures, 9 tables (published version
