I assume it's similar to sheep going to mart - the pig AML form is the same as the two versions ago sheep one.
In which case, the Departure Keeper initiates the paperwork and the Receiver sends the top copy to Trading Standards.
So, welshlass, you would write up the AML, with all your address, holding number, herd mark, the pigs' individual numbers, details of the transport, and the address of the destination. On arrival, the mart staff will fill in their holding number and the number of animals received and give you back your copies. They will send the top copy off to Trading Standards.
When you buy from the mart it's the other way about - they are the Departure Keeper so initiate the paperwork. Most of them are geared up to send your top copy to Trading Standards for you, depending on whether you are in the same region as the mart, but officially I think it should accompany the pigs to their destination and the final section only be completed on arrival.
HTH