Abstract: Methods and apparatus for making an anastomotic connection between tubular fluid conduits in a patient. A connector may provided having an annular structure configured for placement partially within one of the tubular fluid conduits and for annular enlargement by expansion of an expandable structure positioned within an interior portion of the connector. The connector may be configured for plastic annular enlargement, and have members with free end portions that are configured to penetrate a wall of the tubular fluid conduits at locations that are annularly spaced around the connection. A portion of the connector may be selectively deflected radially out from a remainder of the connector in response to expansion of the expandable structure disposed inside the connector.