In order to deauthorize a PS3 that you no longer possess you will have to call Sony Customer Service and they can deauthorize your old PS3. Then you can log onto your new PS3 and download your BF3 DLC from your purchase\download history.
After each expansion has been fully downloaded and installed by clicking the bubbles for each expansion under the games portion of the PS3 XMB start BF3. At this point you will receive a series of pop ups stating that you now have each expansion. Now from the main menu go to multiplayer, open server browser and then open the server browser filter by clicking R3 and check all new maps and game modes or you won't find any games on the new expansions.