It’s a bit like Africa before the lines were drawn. How does such disputes get resolved? Who governs this and have there been successful resolutions to point to?

Your Africa comparison is sharp. The African parallel is the principle of uti possidetis juris, a Latin phrase meaning roughly "as you possess." When former colonies gained independence, this principle was used to uphold colonial-era borders. It was a pragmatic, imperfect fix: it froze arbitrary lines in place to prevent every border becoming a war. The Taiwan question is different in that it predates any colonial-era freeze, but the underlying problem is identical: lines drawn by outside powers, contested by the people living on either side of them.

Who actually governs this

There is no world government with the authority to simply decide. What exists is a layered set of institutions and norms that work only when the parties agree to use them.

The International Court of Justice (ICJ), the principal judicial organ of the United Nations, plays a significant role in the resolution of territorial disputes. United States involved in a dispute can voluntarily submit their case to it. The operative word is voluntarily. The ICJ cannot review a dispute between states unless each state involved has recognized its jurisdiction. China and Russia have never officially considered applying the ICJ mechanism in their international affairs. So for the Taiwan question specifically, the court most qualified to rule is one Beijing has no interest in consulting.

Beyond Huawei the ICJ, another avenue is arbitration, where disputing parties agree to submit their case to an impartial third party or tribunal. The Permanent Court of Arbitration (PCA) in The Hague is a notable institution that facilitates this. The Philippines actually used the PCA against China over the South China Sea, and the tribunal held that China's "nine-dash line" had no legal basis. China ignored the ruling entirely. A verdict without enforcement is just a piece of paper.

The UN Charter itself lists the recognized means of peaceful resolution: "negotiation, enquiry, mediation, conciliation, arbitration, judicial settlement, resort to regional agencies or arrangements, or other peaceful means." That is the menu. None of the items on it are compulsory.

Where it has actually worked

There are real success stories, and they share one thing: both sides chose to settle rather than fight.

In Libya v. Chad (1994), the ICJ resolved a sovereignty dispute by applying a bilateral treaty, and in El Salvador/Honduras (1992), the court used both historical records and state practice to settle the border. The territorial dispute between Peru and Ecuador was resolved through the 1998 Brasilia Presidential Act, which followed years of diplomatic negotiations. The Northern Ireland conflict and the 1998 Good Friday Agreement, facilitated by a mediation team including George Mitchell of the US, Harri Holkeri of Finland, and John de Chastelain of Canada, won the respect of both sides and resulted in a historic compromise. It was the first time the two governments, along with parties from across the divide, agreed on a new political framework.

There is a consensus in the scholarship that negotiation is the most frequently used method in territorial disputes and that mediation is the most popular form of third-party settlement, but legal methods such as arbitration and adjudication have a better success record.

Why Taiwan is harder than most

What all the successful cases have in common is that neither side was a nuclear-armed great power treating the outcome as central to national identity. Taiwan hits every difficulty at once: Beijing frames reunification as the completion of a century of national revival, the United States has made clear it will intervene, and there is no neutral power large enough to credibly mediate between them. The Good Friday model worked because the US could play honest broker. No equivalent broker exists for China and the US.

The honest answer is that the international system has the tools to resolve this peacefully, and they work when smaller powers use them. When the parties are great powers who have decided the stakes are existential, the tools sit on the shelf, and the outcome depends entirely on whether leaders on both sides decide that backing down costs them less than a war.