Final answer:
The structure at the posterior border of a testis that carries sperm to the ductus deferens is the epididymis, where sperm maturation occurs before being transported by the vas deferens.
Step-by-step explanation:
The tubular structure that is found at the posterior border of a testis and carries sperm to the ductus deferens is the epididymis. The epididymis lies along the top and posterior of the testes and serves as the site of sperm maturation. After maturation, sperm leave the epididymis and enter the vas deferens (also known as ductus deferens), which transports the sperm behind the bladder, and joins with the duct from the seminal vesicles to form the ejaculatory duct.
During a vasectomy, a section of the vas deferens is removed to prevent sperm from being ejaculated, thus preventing fertilization. The seminiferous tubules within the testis join together to form ducts that convey immature sperm to the epididymis associated with that testis, whereas maturation of sperm occurs within the epididymis before being stored there until ejaculation. The prostate gland is involved in the production of seminal fluid but is not located in the testes and does not have a direct role in the transportation of sperm from the testicles.