Hello, I have also run into this problem a lot on larger installations (VSX and/or with many in-place upgrades)
It is time they put up larger root partition on appliances by default
For VSX, before R81.20, each VS that has IPS and AMW etc will download the updates into its own context (even if they of course are exactly the same files for all of them)
It is possible to move the directory trees for the update over to /var/log partition, see sk176665.
Be sure to copypasta the script properly (did I say backup first also maybe??)
I have done this on several R81.10 systems without problems while they were up and running
In other ways, since root partition is part of linux lvm it can be expanded, but it may later maybe break upgrades, I have not tested.