Should it stick around until liquidity shows up? (GTC)
Should it cancel any size for which there is no liquidity? (IOC)
Is there such a thing as Market GTC or Market Orders must always be IOC?
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This differs from exchange to exchange but in Toronto (TSX) the rule is that the unfilled amount becomes a limit order at the last sale price.
A market priced order is an instruction to trade the order at prices currently established by the opposite side of the market. Such orders have no trader defined limit on the potential trade price but these orders are subject to TMX bid/ask price limits and TMX freeze price limits to prevent unintentional trade-to-trade price gaps which may otherwise occur if the opposite side of the market is thinner than the trader submitting the market order had expected. If there is not enough volume in the book to fill the order, the unfilled quantity of the Market order is booked at the Last Sale Price.
Having said that, If you have a use case where you are
Let me know so I can either trade against you or get the heck out of your way:)