A growth plate(source: eMedicine)
The prospective zones from bottom to top are the ossification zone, the calcified cartilage zone, the hypertrophic bone, the proliferative zone, and the rest zone(where stem cells are but there are stem cells in other places as well). Really though you can see the overlap of several zones indicating that chondrocytes are remarkably independent.
The above picture is the periosteum to compare to the growth plate. The cortical bone is the solid red zone. To build new bone, osteoblasts simply deposit new bone according to the OPG/RANKL gradient. The fundamental reason why bone deposits beneath the periosteum and not the longitudinal ends of the bones is that they are not ordered to by OPG. The ossification of cartilage provides a signal to deposit new bone. Distraction Osteogenesis also provides this signal. Articular cartilage is at the end of long bones and the reason it doesn't ossify in normal individuals is lack of CD44 and because there's no OPG telling it to.
Here's a larger photo of a growth plate(source: Wikipedia). It may look like a gap but really the two bones are interconnected:
It is possible to grow taller without the aid of a growth plate like in the picture below which illustrates healing by gap fracture.
Now this is a cortical bone fracture. Notice the gap between the two spaces of bone. That gap will not go through the process of cartilage to trabecular bone etc. and eventually become cortical bone(only larger fractures will undergo that process). If that gap occurs horizontally it will result in a slightly taller individual. Over time that could result in a very large height gain. Now if you get microfractures on a smaller scale those tiny little gaps will eventually heal resulting in height gain(albeit an unequal height gain).