I think it takes a few days, not weeksEvery shareholder who oversubscribes is a separate calculation that has to be correct. Also every account you have is a separate calculation.
The allocation is done by eliminating each oversubscriber who gets his allotment, then reallocating among the remaining over-subscribers until they either run out of unexercised rights or there are no more over-subscribers left. In other words, if one guy with 100k rights over-subscribes for 10 shares which is .01%, and everyone else over-subscribed for more than .01%, then this guy is first in line to drop out. If there are enough unexercised rights to give over-subscribers more than .01%, they all get that amount to start. Then the computer looks for the next person to drop and the process continues, over and over. The brokerages have to check these splits so it takes some time before they are comfortable enough with the allocations to put them in each account.
I have rights in 3 accounts at the same brokerage. I wanted to oversubscribe by 12% in total, so to be safest, I went over by the exact same 12% in each account, in case there wouldn't be more than 12% available. If I over-subscribed by 14% in one account and 11% in others and they only had 12% available then my 14% account would only get 12%.