But if they wake up Friday morning with the unprecedented reality of a member state quitting the club, they will have to react quickly to contain markets instability and political uncertainty, as well as to prepare the first steps of the divorce process.
"There are two ways to divorce: an orderly one and a messy one," an EU official said. Although no one in EU circles wants to speak of a divorce, the main institutions believe that the initial reaction could be crucial to avoid the messy type.
The clock will start ticking between 5AM and 7AM British time, when the final results come out. The political decisions at the EU level will then be taken at an EU summit on 28 and 29 June.
But one can expect the following from the European Commission, Council, Parliament and European Central Bank in the next few days.
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