As an aside--remember the theory where urine urate serves as a nidus for calcium oxalate stone formation that you probably learned in medical school? Well, it's probably not correct. While elevated urine uric acid levels do correlate with probability of uric acid stone formation (which is relatively uncommon), it does NOT correlate at all with the probability of calcium oxalate stone formation (the most common form of nephrolithiasis).
In any case, Randall's plaques are calcium phosphate deposits which are thought to occur intraparenchymally, originating at the thin ascending limb of the loop of Henle. These deposits likely grow slowly over long periods of time, and eventually they are thought to erode through the parencyma and into the papilla, where upon contact with the urine they may predispose to stone formation. That's the going theory, at least.