An assembly system for floor and/or wall tiles includes anchors between tiles arranged in a coplanar plane. The anchors are determined from portions curved in the shape of a groove located in the underside of the tiles and matching the side edges of the tiles that guide the curved portions to converge on the edges. When the tiles are put together next to each other head to head and at the point where the corners converge, these curved grooved portions form a channel on the underside of the tiles inside which male elements fit tightly in at least a portion of it to couple and engage at least two adjacent tiles.