BNY is the largest custodial bank in the world. They have something like $40 TRILLION in other people's assets in their custody. The assets themselves would belong to the customers of brokerage houses, funds, institutions, endowments, companies like First Manhattan, etc..
On the A-share volume, I would assume that record high share prices and still-low long term capital gains tax rates have convinced more long term holders (who would primarily hold the original stock) to call the phone number listed in the Annual Report. Berkshire's request was to call either before or after the market was open and we have seen large blocks of A shares cross the 'tape' at the open each day. Consistent with negotiated trades that were worked out before or after market hours. Then that activity draws in more activity as prices rise I suppose
Sorry, I mean First Manhattan bank. 25% of their 13F is Brka ($5b)