So far all the ice *shelves* which have rapidly broken up were already floating on the ocean. For this reason when they melt they make no difference at all to the sea level.
Try this. Place water and an ice cube in a glass. Be sure the ice cube is floating freely. mark the water level. check when the ice has all melted. There will be no change.
Ice floats with about 10% of it's volume above the water because it is less dense than water. when it melts and turns to water it loses that 10% in volume.
One concern is that the ice sheets on land behind the ice shelves may flow more freely to the sea if the ice shelves are removed. I understand that there is some evidence that they are accelerating. If this is true and significant then there is real cause for concern. The, apparently, not so stable west antarctic ice sheet has enough water to bring sea levels up about 20 feet! Many cities would disappear, in fact whole countries! I think Florida is in trouble too. (well maybe only half of it so that's not so bad is it?
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