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?
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.
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:)
As mentioned above, the action depends upon the market. Many exchanges in the USA do not provide the market order type; all orders are priced. The time in force (TIF) is independent of the order type, generally.