Various single-part catheter assemblies, multi-part integrated catheter assemblies, and methods for making the same are disclosed. The single-part catheter assemblies include a catheter hub integrally formed with a catheter tube for insertion into the bloodstream of a patient. The multi-part integrated catheter assemblies include a catheter hub integrally formed to a catheter tube for insertion into the bloodstream of a patient. The catheter assemblies of the invention may be injection molded in a single step or in multiple steps by injecting flows of molten plastic into a cavity of molds provided herein such that the flows converge into an even distribution about the circumference of the sleeve. The mold may have a core pin designed to fit into the cavity. Through the use of the even distribution of flows, the core pin may be seated within the cavity in an untensioned manner. The catheter assemblies of the invention may be produced of a single material or of multiple materials.