From my understanding Peterson traditionally used African Meerschaum for a lot of their meerschaum pipes. Most were made on the Isle of Mann at the Manx Meerschaum Factory. My two Peterson Meerschaum Pipes are African Meerschaum and they are block.
The 1 I still have is African block. But, did buy 1 years ago which was apparently pressed with a threaded tenon. Rather liked it but the the thing got stripped.