The present invention relates to an adjustable star wheel and guide rail assembly for use with containers being processed on an automated handling line between machines such as rotary packaging machines. Star wheels derive their name from their general shape. The star wheels of this invention have fingers that support containers, such that they convey the containers as the star wheel rotates. Conveniently, the fingers of the present invention may be set in any position within their range of movement. In addition, a supporting guide rail may be adjusted, for example by rotation on cams. Thus, the fingers and the guide rail may be set to convey containers of varying sizes while keeping the container's centers travelling along the centerline of the conveyor.