Zechs Marquis of Exeon
Just like Linux has almost entirely shut out the original UNIX's.
Linux isn't UNIX and Linux has in no way "shut out" UNIX.
On the desktop: Unix still has a much larger market share than Linux. Mac OS X 10.5 is a certified UNIX operating system. OS X alone dwarfs Linux usage.
On the server: Linux is again a minority. It's gain a lot of ground on traditional UNIX systems in the past decade, but that's almost entirely due to a fundamental hardware shift. The major cause of Linux server adoption in the corporate world is older RISC-based computing systems being replaced with newer x86-based hardware. It's a fairly recent trend to build super computers around massively parallel x86 processors as opposed to a manufacturers proprietary RISC processor. Previously, when you bought a RISC server, you were forced to use whatever OS the manufacturer supplied you with which was a UNIX system compiled specifically for their architecture. (As an example, look at Sun's Solaris operating system which was created for their Sparc processor). The BSDs have shown more of a serious impact on the server market as their adoption is nearly always based on technical merit and market trends. A number of very high-profile companies like Yahoo! are using BSD on their servers. BSD was on track to completely uproot UNIX in the server environment until the mid 90's when there were some accusations of intellectual property violations and the market lost confidence in BSD. However, it has remained a strong and growing competitor and is very highly regarded by true Unix professionals.
I am always impressed when I get the opportunity to work with UNIX admins because they always know what they're doing. By contrast, I feel the majority of Linux admins are under qualified for their position.