An assembly for forming an interface part for dental implants with variable height, wherein said assembly comprises: - an interface part (1A, 1B) having a tubular shape with a central axis and comprising: a base end for seating said interface part (1A, 1B) on a dental implant body, a pillar for integrally attaching a prosthesis element to said interface part (1A, 1B), said pillar being coaxial with said central axis and extending from said base end to a free end of said pillar, and an inner conduit coaxial with said central axis going through said interface part (1A, 1B) from said free end to said base end forming a passage for a set screw, said inner conduit being provided with an inner rib which forms a seating for the head of the set screw, and - at least one auxiliary part (8A, 8A', 8B) formed for being coupled in a detachable manner to said interface part (1A, 1B), such that in a coupled position: said auxiliary part (8A, 8A', 8B) is coupled to said interface part (1A, 1B) so that it cannot move relatively to said interface part (1A, 1B) at least in a sense of direction parallel to said central axis; a final segment of said pillar, adjacent to said free end, protrudes through an upper end of said auxiliary part (8A, 8A', 8B); said upper end of the auxiliary part (8A, 8A', 8B) forms a peripheral surface outside said pillar, said peripheral surface comprising at least one planar face in a plane; and said plane of the planar face intersects with said final segment of the pillar and said central axis; so that said plane defined by said planar face is a cutting plane for cutting said pillar with a cutting tool along said plane at a specific height which is predetermined by the actual dimensions of said auxiliary part (8A, 8A', 8B), thereby enabling to modify the height of said interface part (1A, 1B). - an interface part (1A, 1B) having a tubular shape with a central axis and comprising: a base end for seating said interface part (1A, 1B) on a dental implant body, a pillar for integrally attaching a prosthesis element to said interface part (1A, 1B), said pillar being coaxial with said central axis and extending from said base end to a free end of said pillar, and an inner conduit coaxial with said central axis going through said interface part (1A, 1B) from said free end to said base end forming a passage for a set screw, said inner conduit being provided with an inner rib which forms a seating for the head of the set screw, and - at least one auxiliary part (8A, 8A', 8B) formed for being coupled in a detachable manner to said interface part (1A, 1B), such that in a coupled position: said auxiliary part (8A, 8A', 8B) is coupled to said interface part (1A, 1B) so that it cannot move relatively to said interface part (1A, 1B) at least in a sense of direction parallel to said central axis; a final segment of said pillar, adjacent to said free end, protrudes through an upper end of said auxiliary part (8A, 8A', 8B); said upper end of the auxiliary part (8A, 8A', 8B) forms a peripheral surface outside said pillar, said peripheral surface comprising at least one planar face in a plane; and said plane of the planar face intersects with said final segment of the pillar and said central axis; so that said plane defined by said planar face is a cutting plane for cutting said pillar with a cutting tool along said plane at a specific height which is predetermined by the actual dimensions of said auxiliary part (8A, 8A', 8B), thereby enabling to modify the height of said interface part (1A, 1B).