A connector for use in providing an anastomotic connection between two tubular body fluid conduits in a patient. The connector is preferably a single, integral, plastically deformable structure that can be cut from a tube. The connector has axial spaced portions that include members that are radially outwardly deflectable from other portions of the connector. The connector is annularly enlargeable so that it can be initially delivered and installed in the patient in a relatively small annular size and then annularly enlarged to provide the completed anastomosis. The radially outwardly deflected members of the first and second portions respectively engage the two body fluid conduits connected at the anastomosis and hold those two conduits together in fluid-tight engagement. Apparatus for use in delivering and deploying a connector is also disclosed.