For such a scenario, there are two most important factors:
- Do you have approval of the government/overlord?
- Do you have popular support within the whole populace?
If you have government approval, you face the same situation a Scotland in 2014. They had the blessing of the UK parliament and were allowed to vote on it. The UK agreed beforehand to honor the outcome of the referendum. There would not have been war, and it is unlikely that there would have been civil war within Scotland.
If you do not have approval, you face the same situation as Catalonia in 2017, when the referendum they held was declared illegal. The Catalan people do not have independence, and in order to break free from Spain they would have to resort to violence. So far, the violence was very limited. This is an ongoing situation.
As far as popular support is concerned, you have Catalonia as example, where the spanish people in general do not want to let Catalonia go. If the catalan independence had vast support in the spanish populace, demonstrations all over spain could help the catalan people to gain approval for a legal independence referendum and force a change.
This happened in Czechoslovakia from 1989-1993. Widespread demonstrations, fueled by the violent suppression of an earlier demonstration with 9 people dead, lead to the fall of the communist government and a new government was installed. Splitting the country had popular support all over the country, allowing a peaceful transition.
So, in order to have a region split from a parent country, you have to figure out:
Why do they want independence? Is there a historical reason? Are there economical reasons? In case of the hypothetical partition of Belgium, historical and linguistic reasons are often cited, but the real reason for wanting to split is economical, the rich regions no longer wish to support the poor ones. The reasons for wanting independence are important because they directly drive who supports them. If a rich regions wants to split from a poor one, then usually the poor one doesn't want that, or if they do, they have to think they can be better off and improve their economy without being part of the larger country.
Who supports their independence? Which internal parties support the independence? Do they have popular support o both sides, if so, why (see above). Which external parties who could have a moderating effect or put pressure on the government support their independence?
What is their bargaining power? A stronger region can easily split from a weaker one simply by the threat of war. If the other side doesn't want independence, but the cost of war is too high, they might not want to do anything about it.
If you look at the pinnacle of "western civilization", the US, you can look at the various bids for Secession of California from the United States. After Trump was elected, secessionist movements in California flared up against after a long history of such movements.
Another problem within the US is the Kingdom of Hawaii. In 1993, the Apology resolution "acknowledges that the overthrow of the Kingdom of Hawaii occurred with the active participation of agents and citizens of the United States and further acknowledges that the Native Hawaiian people never directly relinquished to the United States their claims to their inherent sovereignty as a people over their national lands, either through the Kingdom of Hawaii or through a plebiscite or referendum.". it would be interesting to see what would happen if there was enough popular support within the Hawaiian populace to do something about it. the strategic importance of Hawaii is certainly big, but in times of social media, globalization and internet, can you really rule over a group of island where the people do not wish to be ruled by you and where you already recognized their claim to sovereignty?
Independence and Sovereignty aren't easy, but you can find enough historical examples even in the modern world where you can build upon claims of independence and take it from there. Put more pressure on California, have the US make decisions that are hugely unpopular in California, trash their economy and suddenly it becomes believable in a work of fiction that a few years down the drain the secessionist movement has gained enough support within California to do something about it. find an external actor who wants to help. In the case of the US, that is difficult, because which external actor would risk war with the US to ensure Californias independence? But there are smaller countries where claims of independence exist and bigger external actors might want to help gaining their independence, or where you can contrive a scenario where you have popular support for an amicable split.