Google-chrome – disable incognito mode in ChromeOS (ChromeBook)

OK I'm presuming you;re using Windows...

In Internet Explorer:

Click Start, Run. (or in the search bar for Vista or W7) Type GPEDIT.MSC and hit ENTER Go to:

User Configuration / Administrative Templates / Windows Components / Internet Explorer / Privacy

Turn off InPrivate Browsing:

In Firefox:

Open up your hard drive (c://)(or in the search bar for Vista or W7) through the 'start; run' route. go into program files, go to mozilla firefox, then components.

NOW, make sure you are searching for all files under 'files of type'.

Then, you will be able to see "nsPrivateBrowsingService.js"

Right click and DELETE!!!

That won't remove the controls, but they won't work any more. If you want to hide those Menu items: Add this code to userChrome.css below the @namespace line. See http://kb.mozillazine.org/Editing_configuration#How_to_edit_configuration_files

#sanitizeSeparator, #privateBrowsingItem, #sanitizeItem {display:none!important;}
#privateBrowsingAutoStart {display:none!important;}

Source: http://support.mozilla.com/tiki-view_forum_thread.php?locale=en-US&comments_parentId=378652&forumId=1

In Chrome:

Creating a DWord reigstry key called IncognitoModeAvailability, with a Value of 1 for Disabled in the registry folder HKEY_LOCAL_MACHINE\SOFTWARE\Policies\Google\Chrome seems to disable incognito browsing. Thanks to Imomata for that one.

I'm unable to help you on the Safari one as I have never really used it for any length of time

Unfortunately not. Apps are tied to an email address, and for Chrome OS this would be the user that logs in. Supervised users work differently. They're not tied to an email address and so they cannot install apps. Basically, the two features (supervised users and chrome apps) are built on foundations that don't coincide very well.

The Chrome OS developers are aware of this problem and that many people are interested in this feature, as noted within this Chromium Bug Report

My children also have Chromebooks with supervised user accounts. We maintain a whitelist of sites that they can visit at any time without parental supervision. The problem with this approach, in addition to not being able to install apps, is that the "discovery" factor is destroyed - they don't have the ability to find new sites of interest.

What we've recently done as a workaround is to have monitored time where they are signed in as non-supervised users. On those accounts, we've installed AdBlock Plus, which removes a lot of bad content. Additionally, our router now assigns DNS using the free OpenDNS Family Shield. This blocks access to many many websites that we would not want our children to stumble on.

While AdBlock and Family Shield work well, it's not a fool-proof system. There is still much objectionable content on the web, and even that is subjective. This is why we still choose to monitor their usage during these times.