Hi, Apple will not dominate anything if they release OS X for regular pc's. The first major problem they will face is hardware support. OS X supports pretty much no hardware outside the Mac world.
OS X would not run on any system due to lack of drivers and Apple will have to make majority of the drivers since hardware manufacturers only make drivers for mostly used operating systems. They still haven't started making great drivers for Linux why will they start for OS X? Making drivers is a time consuming task and even the Linux drivers aren't perfect.
OS X would become very unstable because the only reason it is stable now is due to extensive testing on Apple's chosen hardware.
Apple doesn't have the resources to support the entire world and provide support to every system, they will loose their reputation and control which they have on their systems. Not only that but many people won't switch at all since pirated software is not yet there for Mac OS X and many people use pirated software on Windows.
Mac OS X will itself start getting pirated and so will Apple's software and that will be another problem for Apple so they will have to introduce genuine advantage as well.
Apple's computers will not sell much if they release their software for everyone and they focus more on their hardware. Also now that their system will be allowed to run on any system then they will be increasing the risks of people finding flaws in their system and many hackers will target Macs.
EDIT:
LOL....Astro, half of my friends don't even know what the difference between pirated and genuine software is....;-)