There are many causes for short stature in a child. The commonest is that the parents are short. My own area of speciality, endocrine disorders, is the least common cause. The gland which produces growth hormone is the pituitary gland in the brain. Growth hormone is produced by the front end of the pituitary gland, from whence it goes into circulation, and probably directly into the bones, where it stimulates the production of another hormone in the cartilage in the bones.
Growth hormone is secreted in bursts.
Each burst occurs quite frequently in the early phases of sleep, and then later on in the sleep pattern, and also through the day. Growth hormone is made up of many amino acids, but it is now possible to make this hormone artificially. This is done by putting a growth hormone gene into an E Coli bacterium, which goes on to produce a lot of growth hormone. This is essential bio-technology. Incidentally in America, some large trials have been stopped because of an anti-biotechnology lobby.