An implantable tubular textile prosthesis particularly useful in branched end-to-side anastomoses is provided. The prosthesis includes a first portion including an elongate tubular main wall which defines a fluid passageway therethrough, and a second portion including a tubular branch wall which extends laterally from the tubular main wall and which defines a fluid passageway therethrough. The tubular branch wall includes an elongate tubular extent and a contiguous flared tubular extent. The tubular branch wall is secured to the tubular main wall at the flared tubular extent to establish fluid communication between the passageways of the tubular main wall and the tubular branch wall. The flared tubular extent includes a gradual increase in diameter with respect to the tubular branch extent to provide a seamless and substantially fluid-tight transition between the tubular main wall and the tubular branch wall along the flared tubular extent.