My understanding of this teqnique, from reading extensively about it years ago, is this:
The concept, as far as Monty Roberts says, came from a horses flight response, and the natural reaction to a)run in circles, and b)turn to face the danger after a certain distance. In a wild horse(Monty Roberts did a video where he attempted to 'join up' with a wild horse in the wild, by following it until it chose to be with him) that has never had any bad experiences with people, you can put it in a round pen, initiate flight response with a rope, stick, etc, then the horse keeps going until the set distance(I believe monty Roberts says 1 mile?) when the "turn and face the danger" response kicks in. At this point the horse starts thinking about the person in the middle. If the persons body language is right, this happens:
1. One ear locking on you
2. Lowering her head
3. Licking and Chewing
then you invite them (with body language) to come towards you. A wild horse usually, with little work, will take the chance to stop moving and accept you as a non threatening leader, as you are communicating in a language the horse understands.
I have used this on completely wild horses with success. After that application it has little use in my opinion. I tried join up with Romeo, the virtually untouched Clydesdale stallion I halter broke last year. Although he was not halter broke, his limited experience with people was bad. He is naturally submissive and he had almost certainly been squeezed in a chute or flip table to hack off his feet, they tried to use him as a saddle bronc(failure) and who knows what else. He was, and is, very wary and nervous of people, which goes against his calm, quiet disposition. Romeo would not come up to me. He would go, stop, turn and face me, but he had learned people were scary and best stayed away from. He would lick, chew, drop his head, etc. He would even follow, from 20' away. I never got the "instant bond" moment, and to be honest, I don't expect it, with any horse. Just like with people, true bonds take time. Horses that most people work with today have previous experience that hinders the 'join up'.
The big issue for me with join up is the believe that the results will be the same as monty Roberts portrays, untouched horse runs around, magically comes up to you and voila, instant 'bond'! Its also grossly over used. Many people feel they should do it often, like it some how refreshes the 'bond' and makes a horse trust and respect you, without the work entailed to build a real relationship.
Round pen work has a purpose. I use it for a couple initial 'respect sessions' with young hrses, halter breaking untouched older horses, introducing new tack and the first couple rides on a colt(or problem horse). Many people use it constantly, which in my experience quickly becomes a crutch for horse and handler.