How to find out on which partition my home dir is? [duplicate]

Use the df command with the -P flag:

$ df -P /home/
Filesystem     1024-blocks     Used Available Capacity Mounted on
/dev/sda6        913043932 90791288 775849572      11% /home

If home is not on a dedicated partition, you'll get something like:

$ df -P /home/
Filesystem     1024-blocks     Used Available Capacity Mounted on
/dev/sda5         39240312 12539228  24684728      34% /