Underwriting Agreement
  
See: Eastern Accounts. See: Underwriter. See: Syndicate.
The investment bank is the underwriter of the offering. Sometimes, deals are fully pre-bought. That is, the bank actually owns that full suite of securities, just before, five minutes later, turning around and selling them to the Street at a few percent or so mark-up in price.
How the deal is marketed (the price expectation, the volumes, the greenshoe, etc.) are all covered in The Rules of the Game doc that is the UA.