Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

AA's distance-based Explorer award allows a maximum of 16 segments and one open jaw. You may stop over once, and connect twice, at any city on the itinerary, other than your origin and destination.
I don't know whether BA's multi-partner award has the same or different rules. You should prepare a list of your questions and call BAEC back; don't hang up until you are certain that the agent has answered your questions for the particular type of award ticket you are inquiring about.

The oneworld Global Explorer (paid) ticket is a very different animal than BA's multi-partner award ticket. Make sure that the BAEC Service Centre agent knows which one you are inquiring about.

You can also find a lot of information about the (paid) oneworld Global Explorer ticket in a Sticky near the top of the FT oneworld forum (found under "Global Airline Alliances").