The textbook modern example for peaceful splits is the 'velvet divorce' between the Czech Republic and Slovakia. The countries went their separate ways in 1993 after failing to work out a mutually satisfactory system for continuing their union. Despite some tension, they generally enjoy good relations today, with the Czech Republic notably working hard to get Slovakia admitted into the European Union.

Firstly, I'm sure many would contend that the splitting of Sudan has been anything but peaceful and it has kicked off there in the past few months.

The example that is probably most suitable is that of Norway. Norway became part of Sweden thanks to the Napoleonic wars - Norway backed the wrong horse, Sweden invaded and won. The next 90 years of Norwegian history saw the rise of socialism and trade unionism, predating other European countries in the level of their organisation by 50 years. They were fortunate enough to keep their own parliament also so the bureaucratic arms were in place. Communication between Norway and Sweden eventually broke down with Sweden restricting trade with the Norwegians and keeping the union together with threats until, eventually, Norwegians had just had enough. They elected a 4 party coalition in 1905 who attempted to form a consular service (for foreign policy). The Swedes rejected this and the Norwegians took this as the Swedes abandoning their responsibilities in Norway, unilaterally declaring independence. Sweden backed down from threats, insisting only on a referendum on the union - 99.95% of voters voted for independence. While Norway's "subjugation" to Sweden was more akin to Scottish rule in the UK under the Stuarts, with many things still being under Norwegian control, the union did dissolve, and peacefully.