The hair growth will be limited to however long it grew in the donor site. The anagen (growing) phase of the hair cycle is different for different areas of the body. This is why chest hair stops growing and hair from the scalp does not. So depending on where the hair was taken from, that is about how long it will grow.
Transplanted hairs will grow like the hairs from the donor area where the hairs were harvested. It will continue to grow like other hair until you cut it. If the hairs were harvested from the chest it will grow like chest hair. It will not grow like scalp hair.
For donor scalp hair, it will grow for the length of your growing cycle, possibly 2-4 years at 1/2 inch per month. IF you use body hair, it will grow less than 2 inches and then fall out. Only 50% of the hairs from a body donor site, will grow at any one time because of a very short anagen cycle (growth cycle).
An interesting story about Rapunzel I wrote on baldingblog is linked below. Have fun reading it as it discussed how long hair will grow.