Warranty question

Ok, so I've heard talk about the 3rd time you bring your mac in for warranty work on the same problem, they replace it with a new product. What I want to try to get clear is if its the 3rd time you bring it in (fixed twice, third time having the problem) or if its after it has been fixed three times and then breaks (fixed three times, brought in for a 4th).

My macbook is having screen issues and its been fixed once by replacing the HDD but now the problem is back. I want to found out how the replacement thing actually works to see if I can time it with the Leopard release

There is no set rule that a third time in for service gets you a brand new replacement.
To replace a unit with a brand new one is up to the discretion of Apple and the technician overseeing the repair.