It takes the brokerage firms to distribute the shares. Remember, some of the brokerage firms are part of the naked shorting. This means that they have to ensure that the shares in certain accounts are "legit". hint, hint, "covered".
Funny, I asked the same thing and got the responds that they have no controll over the payout of the preferd shares. The dividend will actually be coming from the Depository Trust Company.
DTCC won't be able to send out the divvy shares until the TA sends a cert for them to DTCC.