A starwheel device rotationally transports containers and comprises a body (110) rotating about a vertical axis of rotation, and a plurality of grippers (120), projecting radially at regular intervals from the rotating body (110) and rotating together therewith. Each gripper (120) has a pair of jaws (121) movable towards and away from each other in a tangential direction. A follower actuating member is provided for each gripper (120), which rotates together with the body (110) and is connected to the jaws (121) of the respective gripper (120) and is movable in the radial direction with respect to the body (110) so as to translationally actuate the jaws. A three-dimensional cam has a variable outer cam profile in contact with each follower member and radially acting on each follower member. The cam profile varies depending on the height of the point of contact between cam and follower member in the vertical direction.