Normally, any hair in the scalp has a life cycle, where they grow for 2-4 years (the growing phase is known as Anagen), after which it falls (the falling phase is known as Telogen), but the roots remain and take rest for 2 months (the resting phase is known as Catagen) and then grow again.
Hair when transplanted, usually go into the falling phase, where the hair fall off 2-3 weeks after the operation, but the roots remain, take rest for 8-10 weeks, and then grow back 10-12 weeks after the surgery. This is the normal course. However, due to some medicines applied nowadays, the hairs may not fall, but this cannot be assured. The transplanted hairs will begin to grow 3 months after the surgery, if done properly.