what is the market share of server operating systems - specifically
IBM's AIX operating system relative to other server operating systems
(such as windows, Linux, etc.) Broken down by year for the last few
years (and if available projections for next few years). In addition,
aix server operating system market share within healthcare industry.
An overall Unix marketshare that doesn't break down AIX vs. HP/UX and
other unix OS's isn't helpful.

Youll find it all here at this website of course its for pay only, you
have to pay to get marketing research you know...

http://www.infotechtrends.com

Search for 
Market share of Unix servers by vendor.
Market share of server operating systems by platform. 
Not sure if they have any information about aix market share in
healthcare you can always search for it, but that sounds too specific
And if you graph the numbers in excel you can figure out where these
os's are going without projections, microsoft is taking over anyways.

Have a great day hope this helps.