One interesting remark around the participation in the TAF is why banks would prefer to participate in the European USD auctions instead of obtaining the USD directly from the Fed via their TAF auctions. There are several possible explanations to this. First, and rather obvious, some European banks have no direct access to the Fed and its TAF auctions.
Second, the European central banks participating in the TAF have different lists of eligible  4  BIS Review 107/2008  collateral which for some banks have made the access to USD easier. Third, European auctions for US dollars provide a better timing for European banks. 4.