The connector consists of an annular rigid body conformed to an outer surface
around a wall-opening of a hollow anatomical structure and holding means that keep
the hollow structure adjoined internally to the annular body, wherein a union of
the annular body with another annular body of another connector attached to another
hollow structure forms an inner fluidproof surface that surrounds the abutted cut-edges
of the wall-openings of the approximated two hollow structures. Different embodiments
of end connectors and side connectors in divisible or indivisible unions are provided
for end-to-end and side-to-end anastomoses of various hollow structures.