Growth and maturing of hair post transplant?

The short answer is generally 9-18 months.  It depends on what stage in the hair's cycle that follicle was removed and transplanted in, how much trauma it received from the procedure, how fast your hair generally grows, etc.

In general, it takes about 6 to 12 months for the newly transplanted hairs to start growing.  Sometimes longer or shorter.

Here is how I can sum up the life cycle of a new hair after hair transplant:A transplanted hair initially goes to resting phase in most cases.  That means its hair shaft falls while the follicles stays in place.  It takes 2-3 months for a new hair to start growing.  At the beginning the new hair is tiny and resembles a miniaturized hair.  This miniaturized hair becomes thicker and longer over time.  At 6 months most hairs are out but they are still short and need to grow longer to provide the bulk and coverage to the balding area.Most people can expect full growth at 12 to 18 months from a hair transplant surgery.

It is perfectly normal for transplanted hairs to fall out after 1-2 weeks. You may not see any re growth for 3-4 months and then it may be another 3-4 months before the new hairs have strengthened enough to make an early judgement on the result. It might be a further 12 months before the hairs are fully mature.

Once a transplanted hair emerges from the scalp it takes about 9 more months on average for it to grow in length and calibre sufficiently to blend in with existing hairs. 

The it grows to some length that is intrinsic to each hair and then goes through a rest phase to just pop up and grow again. 90% of the hair in the head grows all of the time, the 5% rest and then start growing again. This is the normal cycle we see in hair. If your hair cycle is very long (growth cycle), then it could grow to a few feet in length, but most men have a 3 year hair cycle which produces 18 hair length. 

Each hair has its own intrinsic hair cycle. After hair transplant it goes through its own cycle of growth.  There are three cycles growth stage, the resting stage, and shedding stage.  If the hair is in the growth stage it will start to grow in sooner than if it is in the shedding or resting stage.  Usually after three months the new hairs will start to grow in and may take up to 18 months for all the transplanted hairs to grow in. However for each transplanted hair to take its natural characteristic takes any where between nine to twelve months.  During this time, you need to be patient. Keep in mind that as your hair is coming in, you are naturally losing some hair and also some of your hair is going through its cycle as well .  This is an on going process.