How do I get around "No space left on device" message while backing up in single user mode?

Hi all,

I have a 27 inch iMac (year 2011 I think)

1TB storage

4GB RAM (I think)

Apologies for not being sure--I recently upgraded to Yosemite and encountered the boot loop and white screen so many people are talking about, and now can't even start my Mac properly to check for the right details. I tried every way I could find online to get it to work (recovery mode, pressing the alt key, safe boot, reset PRAM, fsck...) but it was still always a guess as to whether it would start up successfully or not. I have decided to downgrade, back to Mavericks, which my it worked fine with before.

I used single user mode and followed the instructions at: http://thinkinginsoftware.blogspot.com/2014/03/mac-osx-not-booting-make-backup-f rom.html

The device where I saved (or would have saved) my backup is a WD My Passport Ultra 2TB external hard drive. It was clean and had nothing on it after partitioning (1 partition; Mac OS Extended (Journaled); GUID Partition Table).

The last thing I entered (minus the # at the beginning) was:

# cp -r /Users/name-of-user /name-of-ext-drive

It seemed to be working and ran for about 15 hours but I woke up this morning and saw white text running down continuously, listing the files with a message at the end of each: "No space left on device". The light on the external drive had stopped flashing as well and when I unplugged it and checked it on my other computer there was only 4KB of free space left. I checked the files and recognized that they were from my Mac, though there were so few they didn't seem enough to take up 2TB of space.

At the risk of sounding ignorant, I'd like to ask: can someone please explain how it happened that a 2TB external drive ran out of space while backing up a 1TB Mac? I'm guessing it's because I entered the entire name of user which included a whole ton of "hidden" system files I don't normally encounter, but I still find it strange that it seemed to take up an entire extra terabyte on the external drive.

Also, I'd like to ask if there is a solution for this. The external hard drive is now clean (again) and I'm planning on starting the backup process over. Perhaps I should backup the folders under name-of-user instead? Eg:

# cp -r /Users/name-of-user/Downloads /name-of-ext-drive/

# cp -r /Users/name-of-user/Documents /name-of-ext-drive/

# cp -r /Users/name-of-user/Pictures /name-of-ext-drive/

# cp -r /Users/name-of-user/Movies /name-of-ext-drive/

# cp -r /Users/name-of-user/Desktop /name-of-ext-drive/

I appreciate any advice.

Thanks,

Mia