1. The tablet should be already upgraded to stock ICS for A100/A101 (or stock ICS A500/A501/A510 for other tablets).
2. Download this archive on the computer. Unpack it to any place.
3, On a tablet: "Settings" -> "Applications" -> "Development" -> "USB debugging" switch on.
4. Сonnect the tablet to the computer (Before connection it is recommended to update the driver for a tablet from here: A10x, A50x, A510).
5. Open the directory with the unpacked archive. Execute file: for windows - runit-win.bat; for Linux - runit-linux.sh.
The root is received!
6. Now you will have to install the following programs:
At first it is necessary to start the Superuser program, at least 1 time after receiving root. And only then programs that require root access.
Don't install Busybox! It is already installed and established! If you reinstall it, some programs will become unable to access root permissions!
The error of final check of receiving root is corrected (The messaging that "root" isn't received, though it was not so)
Support of A510 of tablets is improved
This method uses the 'mempodroid' exploit and some workings out by ZeroNull and vdsirotkin (4pda.ru).
List of rooting versions:
New - ICS_rooting_A10x_A5xx.zip
Old - ICS_rooting.zip
PS: I understand English rather badly, but I'll try to help, if it is necessary.
PS2: Command "Mount ro/rw" for directory /system (partition) - works perfectly!
PS3: This method does not work on the A511 tablets