BERLIN — When exactly should the British leave? How should the European Union react? Following the initial horror at the UK vote in favor of Brexit, the search is now on, from Brussels to Berlin and beyond, to find practical solutions to pick up the pieces and set Europe on a new path forward.

Here are some of the big, hard questions EU leaders must face:

When? Most European leaders say the UK's exit from the EU should happen as soon as possible. EU Commission President Jean-Claude Junker was asked when? "Immediately, now would be good." French Foreign Minister Jean-Marc Ayrault and his German counterpart Frank-Walter Steinmeier both warned against Britain "lingering," urging a rapid start to negotiations for the terms of the exit.

European leaders fear, above all, that any period of uncertainty raises the risk that other countries might follow the UK's lead in leaving the EU. But it's also in the interest of many nations to put uncertainties aside, as soon as possible, in order to limit the damage of the British decision. Stock markets across the world sank in the immediate aftermath. Meanwhile, France is preparing for the presidential election in 2017, and Germany for parliamentary elections; and Pro-EU parties in these and other countries will face many questions about the consequences of Brexit.

But there is another view, mostly clearly articulated by German Chancellor Angela Merkel, that rushing through negotiations would be a bad idea, that the parties need to "first calmly analyze the situation."

What new EU? There is one thing all seem to agree on: The European Union must change. But the "how" is the hard part. There are those who clearly request "more Europe," others are more cautious. European Parliament President Martin Schulz belongs to the first group. He recently published a 10-point agenda for deeper economic integration among European Union countries, which includes a common fight against the troubling high youth unemployment rate in Europe. European member of parliament from Germany Elmar Brok also asks for "more," notably on the terrain of military affairs.

The French and German foreign ministers have already laid out a common paper, invoking EU member states to focus on specific topics and tackle some of the big problems that must be addressed. Ayrault and Steinmeier are focusing specifically on counter-terrorism coordination, immigration and the economy, giving the option for member states to commit to certain criteria according to different calendars, bringing back the old idea of "two-speed Europe." European heads of state are balancing any desire for deeper integration with the realities of increasingly Eurosceptic forces inside their respective countries.

What new EU-UK relationship?

This may be the most important and uncertain question in the wake of the Brexit referendum. On the one hand, Britain represents an important political and business partner for many, including Germany, encouraging the maintenance of strong cooperative relationships in the future. That's what Angela Merkel wants. But if the treatment of the British after their exit is too generous, it might lead to Brexit imitators. Among the scenarios for the future relationships with Britain being discussed right now: Should the UK be granted a similar status to Norway's, a member of the European economic space with unrestricted access to the European domestic market? Or should there be a close partnership based on a series of different contracts and agreements, similar to the EU's dealings with Switzerland? But German Finance Minister Wolfgang Schäuble takes a very different approach, calling for a "privileged partnership," like the one discussed with Turkey. That would teach a hard lesson indeed, leaving the British Isles farther away from the European Union than Switzerland or Norway.