Is this correct:?
Training the center through methods such as ki-breathing and visualisation of imaginary ether condensing into your hara, trains one's sensitivity with the center and conditions it such that it can better serve as a "junction box" controlling (i.e. direction and power control) of the long whole-body connection vectors.
Of course if your "transmission system" (the rest of the body) is crap (e.g. not relaxed, unable to maintain the state of fully relaxed connectedness) then you've still got nothing even if you have a strong center since the force vectors just get cut off in the tension spots. That's why we train for relaxedness first and foremost.
Please correct my misunderstandings!
Well... That's what I've been told in aikido, but I don't buy it anymore. Tension is critical in my view to creating a transmission system (to use your phrase). The difficulty comes in learning what kind of tension to create and how to maintain that tension rather than a goal of eliminating all tension. If you've read Rob's posts on some of the Aunkai methodologies, you are generating quite a bit of internal tension in many of the exercises. Now, as to whether or not that's a part of aikido (or should be) is certainly a huge point of contention. It's a big part of whatever I want to call what I'm doing these days however, and I can make my "aikido" work better when I do it this way.