How does the human liver regrow?
At least 25% of the original liver seems to be the minimum for regrowth.

The initial regrowth is due to proliferation of hepatocytes: they exit G0 and enter mitosis. The ECM dissolves and is remodeled; the cholangiocytes and SECs also divide. 

If you want to read more, you can visit the Google books link above, and the preview lets you read several pages on liver regeneration in rodents.  (If it doesn't work, try changing the URL to your current location: books.google.com is US, books.google.ca is Canada, etc.)