That depends. If they were buying direct from say Apple (or anyone else with a large block to sell) then they would arrange a "Fill or Kill" order - which is a exchange order type specifically for this large deal (a bit anti-market really) - basically Buffets broker and Apples broker talk on the phone and arrange the deal at a certain price and time. Buffets broker sends in an order to the exchange asking for 1.3m (or whatever) shares in Apple at 600usd and the exchange will only fill orders that take the whole - that is it does not sit there getting a 100 shares at a time, but is waiting for someone else to fill the whole lot. The other sides broker then takes the whole order about 30 seconds later and they all go to the pub.
Source: listening to people who actually know what they are talking about. I may have mis-listened.
My understanding is that Fill or Kill doesn't require a single fill, merely that the entire volume is instantaneously filled.
So, if I send FoK Buy 100 shares @ 500$, then I could end up with 100 fills of size 1, or 1 fill of size 100. It makes no difference (except occasionally in commissions/costs depending on exchange). However if there were only 99 shares it would not partially fill, and would simply cancel unfilled.
Immediate or Cancel would allow you to get "up to 100 shares at a price of 500" and cancel instantly once available volume was consumed.
Source: listening to people who actually know what they are talking about. I may have mis-listened.