I found an article about the Thunder Horse play (first deepwater site) and they talk about all the challenges to bring it online, all the new technology that had to be developed, etc.
In the article (from 2009) it said they commonly dealt with preasures of 18,000 psi, and each well was producing 50,000 barrels/day - with numerous production wells per platform. They also talked about water injection to increase the pressures/ flow though. Not sure if that comes into play when the well is still new, or after the natural flow goes down or not.
Ordinarily, as the pressure in the reservoir drops, the flow decreases, to the point that at some point the well has to be pumped (oil no longer reaches the surface on its own).
The oil industry is one of constant innovation and design, and the time needed to drill a well has been cut to 1/4 what it was just 30 years ago, not to mention that we have the ability to drill (and steer as we go) directionally and horizontally as well.