Nope. Yes, market orders are fast because they are essentially instant.
I've done it a few times long ago, and you can watch it walk the price down. I sold 44M shares of bvtk at market just to get the cash I needed and get out of bvtk while the getting was good. Each tranch was lower than the previous one. I could go back and find that transaction, but I'm not gonna.
MMs have a bid/offer and QUANTITY. Each time they fill an order for that quantity, they can change their spread. That's what they do with large market orders.
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