It is the clearing house for the markets. DTCC has actual ownership of every public stock in the United States (and possibly other countries).
Ready for this? dah dah. DTCC is owned by the Federal Reserve.
DTCC issues electronic BENEFICIARY rights to shares to brokers which is what actually gets exchanged on the market, but DTCC remains the actual and legal owner of the paper.
In other words we kind of have a "free, capitalistic" market by POLICY, i.e. by FED and government policy, which of course could be changed at any time.