When you get your 12 atma items, you turn your Zenith relic into an Atma relic. It keeps the same stats as the Zenith, and has its iLevel raised to 100.

You then need 13,500 tomes to purchase all 9 books. Each book you finish increases its associated stat on your Atma relic. When all 9 books are finished, you go back to Jalzahn and he will upgrade your Atma to an Animus.

Here's a nice FAQ on the Zodiac weapons.