Sadly Ubuntu does not have LVM enabled in the default install, as this whole issue would be solved with a simple pvmigrate and lvresize...
My /home (which is on a separate /dev/sda5 partition) is filling up.
The availability of Steam on Linux gave it the final blow: it's time to bring in another partition.
As I don't want to commit a whole partition to /home, I've mounted /dev/sdc2 as /space and I'm going to create a symlink to an home subdirectory.
First, boot Ubuntu in rescue mode and select root shell.
Mount all filesystems
note that mounted filesystem won't be visible with a df, but you should cat /proc/mounts to see them
Set proper permission to the new partition
#chown root:root /space
#chmod 755 /space
Then create the new home and copy the old one
#cp -a /home/* /space/home/
Mount / read/write as we'll need to modify the fstab
#mount / -o rw,remount
Comment the old /home
Remove the old home mount point and create the new symlink
#ls -s /space/home /home