There are no "three central governments." However, there are the Three Great Powers. The World Government believes that if the balance between these three powers shifts at all, then the world might fall into chaos.
The three powers are as follows: 1. Marines - These are the main "Peacekeepers" of the World Government. Luffy has fought one of the three Admirals and lost (Aokiji) 2. Shichibukai - Also called the Seven Warlords of the Sea, these are seven pirates who essentially become Priviteers in the servace of the World Government. Luffy has met all but one of them (Doflamingo) and has befreiended/allied with two current (Hancock, Jinbei) and one former (Crocodile) members. 3. Yonkou - The "Four Pirate Emporers." They are widely considered the most powerful pirates in the world of One Piece. Luffy has connections with two of them: Whitebeard is Ace's (Luffy's brother) captain, and Shanks was the one who inspired Luffy to be a pirate as well as the one who gave him his signature straw hat.