What does influence hair growth?

No one can answer this question with certainty.
What we do know is that it takes a lot to stop hair growing!

General health and nutritional factors are increasingly believed to be important for healthy hair growth. We do know that serious anaemia affects hair growth. So too does starvation: people who go on a crash diet may start to lose their hair some six to ten weeks later. Many alcoholics have poor hair growth or even hair loss because their way of life tends to lead to malnutrition.
Some minerals may be particularly important for hair growth. For example, some people who lack zinc in their diet produce only fine, sparse hairs and even lose their hair. Vitamin B, also known as panthenol, plays a part in hair growth. It also improves the physical properties (elasticity, strength and gloss) of the hair shaft.

The hair cycle for each individual hair is influenced by the levels of various hormones in the blood. Thyroid hormone speeds up growth in resting hair follicles. Steroids taken by mouth slow it down, though steroids inhaled for the treatment of asthma do not affect hair growth. The hair of the scalp is, however, most sensitive to the effects of male hormones (androgens), which are in the blood of people of both sexes (only in different proportions in men and women). Androgens are the most important factor regulating hair growth, and also the thickness of the hair shaft. Female hormones (oestrogens), which both sexes have too, slow down hair growth during the growing period but also make that period longer. Many women notice a difference in their hair growth during pregnancy. At this time women have vast amounts of oestrogen in their blood, far outweighing their male hormones. It is the balance between the male and female hormones which decides the growth of the hair. At puberty the immature vellus-like hairs on our bodies can change to terminal hairs. This change results from the dramatic rise in androgen levels at that time. It is especially noticeable in young men. Young women who suffer from the condition of anorexia nervosa, however, stop having periods and produce very little oestrogen: their natural androgens tend to thicken their fine vellus-like hairs in the same way.

Treatment of cancer with drugs also influence the hair growth. It may even cause apparent complete hair loss.This is because these drugs are designed to kill cancer cells, which are cells that are growing out of control. Other cells that are growing very actively may be affected too: these may include cells in the bowel lining and also in hair follicles. This leads to a 'break' in growth and an inherent weakness. Once the drugs are stopped the patient's hair starts to grow back, but when it reaches the surface it tends to break. This is what causes the apparent hair loss. The hair that subsequently grows may look quite different from the old. This is because the growth patterns of the sensitive cells of the hair bulb may still be upset by the effects of the drug.
Experiments have established that there is also the link between the immune system and hair growth cycle. Significant hair loss can also be caused by severe psycho emotional stress.