How to completely disable Ubiquity (iCloud syncing?) in Mavericks or above?
There isn't an "ubiquity" you can simply disable IMO. I would exhaust other avenues of solving this problem. Random shutdowns are irritating, but the best thing I have is to train the user to:


Get sysdiagnose each time it happens. (or right after the reboot / when the problem is noticed)
Log the date and time of the error on a piece of paper


Establish that you will review the results every 10 instances. Once you have 10 to 30 reports, you'll know quite certainly if there is a pattern or if there isn't. Also, you'll have enough logs to report a bug to Apple or open a ticket to get AppleCare (or whomever you pay for support) to look at the details and get a fix/suggestion. Without data, you'll be chasing phantoms and get so desperate you'll want to cut out the guts (or hopefully just an unused appendix) of an OS in hopes it will help.