Adobe Update is a rather annoying piece of useless code that sits in your menu bar and lets you know that there are no updates for your software (I run CS5 still). There are lots of tutorials on how to disable the notification icon, but nothing–especially from Adobe itself–on how to remove Adobe Update from OSX entirely.
After a good bit of digging, I came across this blog that led me to the answer. He goes into a bit of detail on how the process launcher in OSX works (and it’s a good, short read), and the execution of the underlying code. I certainly recommend taking a few minutes and reading about it so you can apply the principle for other “unnecessary” applications running in background.
What you essentially want to do is open a Terminal session and type the following series of commands:
basename com.adobe.ARM.* .plist
This removes the process’s associated files as well as the entry from the launcher. Conversely, you could simple navigate to the same folder in Finder and delete the files manually, but it leaves the process entry in the launcher–which may or may not be an issue. I did it this way and have not experienced any problems, but your mileage may vary.