This is what I've found so far. I think a couple of these are hidden as I can not see them in the Finder but I can find them with an uninstall utility. I will try to find a utility that shows me hidden files on a Mac.
/Applications/Media Center 18.app (File)
/Applications/Media Center 18.app/Contents (Folder)
/Users/XXXX/Library/Preferences/JRiver.Media-Center-18.plist (Hidden File?)
/Users/XXXX/Library/Saved Application State/JRiver.Media-Center-18.savedState (Hidden Folder?)
/Users/XXXX/Music/JRiver Conversion Cache\ (Folder)
/users/XXXX/Documents/JRiver (Folder)
/Users/XXXX/Library/Application Support/JRiver/Media Center 18/Library (Folder)
Ahh, yes. I didn't remember the stuff in Documents (and the Cache folder if you have that enabled). You can leave those there, though. That's just media files and Library Backups.
Also, don't mess with the SavedState files directly. OSX creates those itself (it is an OS function, not an application function) and handles them. If you ever need to clear the Saved State for a specific app, you
can follow these instructions, but generally, ignore them. I'm pretty sure MC does NOT use the built-in Saved State system, though, so it whether the file exists or not won't have any effect on MC (and the OS will just make another one the next time you run it). And, lastly, just so you know... This:
/Applications/Media Center 18.app (File)
/Applications/Media Center 18.app/Contents (Folder)
These aren't separate "things". On OSX, Applications are a special filesystem concept called "bundles" (or packages) that Windows doesn't have, but they are essentially special folders. All Applications (and other stuff too, like pkg files), are these bundles. You can right click on them and pick "show package contents" to access the inside of the folder. However, if you check them out on the shell (in Terminal), you'll see that as far as the underpinning UNIX system is concerned, the "files" called X.app are just plain old folders. The Finder shows them as "files" and allows you to do an Open command on them to execute the application it contains, but they are folders.
That's what the application is. Sometimes opening them up and looking at their contents is handy. You can customize some applications this way (things like icons, artwork, and whatnot), and you can often find handy stuff. That's how, for example, you can get the real OS installation DMG (to save or make a bootable USB install/recovery disk) when you buy Mountain Lion from the App Store. Likewise, it is handy with Parallels and VMWare Fusion to grab a copy of the VMWare/Parallels Tools DMG files (essential for making a "hackintosh" VMWare install of Mountain Lion on VMWare Workstation on Windows). Junk like that is hidden in there (application resources), but usually opening them up is fairly useless unless you intend to hack around with (or attack in some way) a particular application.