Kuní was formerly part of the German Empire. In the German Empire, the place was called Kain.
The place is now abandoned and the area belongs to Czech Republic.
| Historical place name | Country | Administration | Time |
|---|---|---|---|
| Kain | Austro-Hungary | Neuhaus | before the Treaty of Saint-Germain |
| Kuní | Czechoslovakia | Jindřichův Hradec | after the Treaty of Saint-Germain |
| Kain | Czechoslovakia | Jindřichův Hradec | after the Treaty of Saint-Germain |
| Kain | German Empire | Neubistritz | 1938 |
| Kuní | Czechoslovakia | Dačice | 1945 |
| - aufgelassen - | Czechoslovakia | Jindřichův Hradec | 1992 |
| - aufgelassen - | Czech Republic | Jindřichův Hradec | 1993 |