A set for manufacturing a threaded connection, including first and second tubular components with an axis of revolution, one of their ends including a threaded zone formed on the external or internal peripheral surface of the component depending on whether the threaded end is of male or female type, the ends finishing in a terminal surface. The threaded zones include, over at least a portion, threads including, viewed in longitudinal section passing through the axis of revolution of the tubular components, a thread crest, a thread root, a load flank, and a stabbing flank, the width of the thread crests of each tubular component reducing in the direction of the terminal surface of the tubular component under consideration, while the width of the thread roots increases, profiles of the load flanks and/or the stabbing flanks of the male and female threaded zones, viewed in longitudinal section passing through the axis of revolution of the tubular components, each having at least one identical portion such that the male and female threads can be fitted one into the other over the identical portions when the first and second tubular components are made up one into the other. The identical portions of the male and female ends are radially offset with respect to each other.