My old broker (maybe 15 years ago) said that after hours market trades were made if a broker (examples; Morgan Stanley, Schwab, Fidelity) had an "in house" match up of buyers and sellers. They were the market maker and made the trade after hours if both sides had open positions during after hours. I think that is what he said. Again this was many many years ago. Just wondering to your knowledge how does it work today?? Do after hours bid/asks go to a in house routers? Does it stay with the in house broker? Does it go to many routers and many brokers? Could you end up with odd lots (stocks) in an after hours trade? Do I have to get an OK from my broker to (in the future) enter into after hours trades?? Was watching TSLA today at the end...Was curious what it would do after hours...
As two examples, NASDAQ and ARCA, allow trading from 4am to 8pm ET. You need traders willing to trade with you. Either customers or firm BDs. Most of the trading looks like they are customer and institutional limit orders. Most equity MM stop trading at 4PM. If have to ask your broker if they allow trading outside market hours. We do.
All I know that IB doesn't allow market orders for after-hour trading. I dunno if that's an exchange rule or an IB rule. I always thought it's the exchanges' algorithms that would match up the buyers and the sellers on the order book during after-hour trading.