As of today, March 18, 2013 Alphaliner estimates the world's Liner Shipping to amount to 5,925 ships active on liner trades or 16,943,189 TEU; including 4,944 fully cellular ships or 16,474,446 TEU.
Their Top 100 list of the carriers is based on the sheer TEU power of a liner company. The Top 30 is shown as following: