A System of Triple abutments with Tconnect comprising T-abutments to place at least three dental crowns over a one only osseointegrated implant and only one T-abutment, for partial fixed cases and new total fixed segmented cases, T-Over abutments with Plug T for use of overdentures over only one abutment and only one osseointegrated implant too, T-healing for guide specific gingival contour of the Tconnect in the healing phase and T-guides, to guide the implant surgery to be positioned for the use of abutments of this system. The all abutments of this system has Tconnect, being an exclusive design support with paraboloid multidimensional contour in double shape curvature with three pins disposed in the form of a tripod (in triangular arrangement) and are adaptable to all the implant/abutment fitting connections of market. All system may be individualized, make in process type CAD-CAM or prefabricated (manufactured type) and it can receive any type of surface treatment. The new biomechanical possibilities of the invention provide stability, passivity, greater precision of adaptation and better distribution of tensions, a fundamental advantage for use of the immediate load. The soft tissue is favored by immediate loading too. The new fixed arrangements with segmentation promotes cleaning and longevity for the system. This invention provides superior resistance of the abutments, long-lasting esthetic and reduction of the bone grafts, clinical time and costs, ensuring predictability of the results.