Part of the problem is due to the Nabi 2's file storage system. Instead of its external storage being located at /mnt/sdcard, it is instead at /mnt/sdcard2. This causes problems as many programs will assume they are saving to the external drive at sdcard, but are instead using precious space on the limited internal drive.
There are a couple different work-around rooted options, but at this time they seem to me a bit like a bandage. If you feel like tackling these more advanced drive swapping options, see Root External 2 Internal SD (How-to for Nabi 2 by e2950) and DirectoryBind by slig (How-to for Nabi 2 by Clarkiss). Root External 2 Internal SD swaps the two. DirectoryBind causes apps to install their extra data to sdcard2.
The first thing to do when you've got a failure to install an app due to insufficient space is to check the device's storage. Get there by accessing Android's Settings, Storage, and when the graph and list come up on the right, touch Apps. You can sort by app size or by alphabetical. Sort by size and the list will show which apps are taking the most space. Another way to get to the same place is via Android's Settings, Apps, and select All at the top.
A. Easiest is removing unwanted demos and preinstalled apps. Touch the name of the app and select Uninstall. I am unsure if this will require root or not. I didn't try while still unrooted and don't know if some apps are locked in by Fuhu.
B. My first space hog was actually the Gallery. One of the first things we do after getting recovery and root on the Nabi 2 is to install GApps. In doing so, Google's Gallery replaces Fuhu's. I have uploaded many Picasa albums over time and, using my Google account on my son's Nabi 2, syncronized and downloaded 300 MB onto the internal storage.
Unsync and clear Google Gallery:
1. Open Android's Settings, Accounts & sync, [Your Google Account], Uncheck Sync Google Photos
2. Settings, Storage, Apps (All), Gallery, Force Stop, Clear Data
After rebooting, the downloaded albums and photos Google had sync'd will be gone, freeing up precious internal space.
Update: More picture/video space hogging was found in /mnt/sdcard/DCIM/.thumbnails There were two thumbnail files adding up to 277MB hiding out.
C. Having multiple rooted android devices, one of the first things I set up after rooting is Titanium Backup (TB). Normally, TB saves its backed up files to sdcard. But, because sdcard is the Nabi 2's space constricted internal storage, this causes a problem quickly. The solution is to change TB's backup storage location. This can save hundreds of MBs. This was the first problem I tackled, so I don't remember how much
1. In Titanium Backup, open Preferences, Backup storage location
2. Change the default location from /mnt/sdcard/TitaniumBackup to /mnt/sdcard[BOLD]2[/BOLD]/TitaniumBackup
TB will handle copying your contents from the old directory to the new one.
D. My next surprise space hog was cloud storage app Box. Hogging a respectable 138 MB of files apparently sync'd/cached, this one was easy to clear.
1. In Box, open Settings, and touch Clear Cache under the Folder Activity heading.
These are basic, simple, and temporary tips which will only free a little more space to allow installation of that one last app you mean to get on your Nabi 2. Any other suggestions would be more than welcome.
I'm hoping that as the Nabi community matures and XDA grants us our own subforum (hint: lets do our best to stoke more Nabi 2 threads), that solutions are created to truly fix the lack of space to make this device pain free and open up its true potential.
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