An implanted intervertebral prosthesis includes first and second components adapted to attach to a first vertebra and a second vertebra, respectively, that define an intervertebral space. The prosthesis includes a first anchor structure on the first component adapted to enter a grove formed in the first vertebra, and a second anchor structure on the second component adapted to enter a grove formed in the second vertebra. The first anchor structure is offset from the second anchor structure to provide separation of the grooves to preserve vertebral thickness and avoid vertebral splitting. The offset anchor structures can be symmetrically disposed about a midline of the prosthesis or asymmetrically disposed about the midline. In some embodiments, the offset anchor structures comprise elongate anchors shaped as fins or keels. In other embodiments, the offset anchor structures comprise rows of pillars disposed in rows.