A high-viscosity polyamide composition including a branched polyamide is described. Also described, is a relationship between a high-viscosity polyamide composition and a composition including a copolyamide of a statistical tree type resulting from a reaction between a multifunctional monomer including at least three reactive functions in order to form an amide function. Further described, are three reactive functions of two different types and bifunctional monomers used in the manufacture of linear polyamides. A resulting copolyamide can have a very low melt flow index relative to the linear polyamide and improved impact resistance properties. Lastly, use of such a composition for extrusion blow-molding articles is described.