I’m just documenting this because i’m sure someone else will have the same problem, while installing the Windows ADK for a Configuration Manager 2012 SP1 upgrade on another server I got an error at the end of the ADK setup log file Assessment and Deployment Kit_2013021020493.log found in %temp%\adk\
Exit code: 0x80070070, restarting: No
and the reason was lack of space on Drive C:\ during ADK installation (as it needs to extract some files during setup.
I had something like 1.24GB free on the C: drive. After freeing up some space (6gb) all went well