HPTA Development
So the HPTA is composed of Hypothalamus, Pituitary, and Testicles. Developing of the hypothalamus and the pituitary mainly entails that the hypothalamus can produce GNrH to an acceptable extent, then moving on to the pituitary gland that is responsible for LH and FSH production. I would think it is logical and fair to say that once the hypothalamus can produce GNrH and the pituitary LH/FSH to an acceptable state that they are so called "fully developed." Testicles descend in puberty and they are responsible for testosterone production as well as sperm. Once they are fully capable of pushing out testosterone/sperm I would once again say it is fair to say they are fully developed.
To measure development of puberty they use the Tanner Stages. When a male is a certain age and doesn't belong to the proper Tanner stage you can suspect a problem in development. In the case of a problem, there are a number of drugs and AAS to use to help increase the development. CBS had a so called "micro-penis" as a late teenager but was able to use Proviron to help grow that little pecker.
You have fully gone through puberty and become a man once you reach Stage 5. This is a measure of puberty, and puberty is controlled by hormones. I would say that the Tanner Stages are reflective of the development of your HPTA. At 15-18 your penis and balls should be fully developed and producing a lot of testosterone as well as 1000 sperms/minute.
That is a picture as you can tell of the balls and penis only. There are other pictures as well of how the rest of the body should look like but for CBS enjoyment I chose the male genitalia only. The tanner stages also apply for females and they have pictures of development as well.
In the bodybuilding community people frown upon young guys using AAS and cite some random article of a vague description to why the HPTA is not fully developed. Ask further and in greater detail and as you have already gotten from previous members they are unable to answer the question for one reason. They don't know what they are referring to...
Worthy of note, growth plates fuse in late teens and early 20's. However, the reason for growth plates to fuse early is an increase in estrogen. This is a reason to why women are so much shorter generally speaking because they have higher amounts of estrogen. If you are concerned about this, you can use an AI to keep growth plates from fusing prematurely.
Mad scientist: During puberty, I would hypothesize that if you use an AI you will get an increase in testosterone which leads to a larger penis and the decreased estrogen would lead to growing taller. I would love to experiment on little Eskimo children to see how you could alter their growth from the norm.