Abstract: The invention relates to a connector (1), applicator and method for mechanically connecting hollow structures, in particular small blood vessels, in order to make an anastomosis. The connector incorporates various features to create a reliable engagement with the vessel walls to make a good connection thereof. The applicator may comprise knife members to make an arteriotomy and punch a hole in one of the vessel walls, comprises an expansion portion to cause a large expansion with a minimum profile, and comprises anvil members to reliably bring staple-like elements (5) of the connector to the joining position. The invention also includes auxiliary devices such as a punch and deforming instrument.