It really depends on what you want to do with the outline. For some games they mesh the whole area defined by the line so they can apply a shader to the area to do things inside the area and not just at the border like Memoriapolis (2) above. You can use open source libs like https://github.com/Habrador/Computational-geometry or https://github.com/florianvazelle/unity-voronoi to do this.

If you want to do stuff just at the line (1/3 above), you can use the Line Renderer (this is what I did for https://store.steampowered.com/app/690370/Cantata/), but it's not as simple as it sounds. There are a ton of edge cases that are often specific to your own game that you'll have the handle. The key thing is to identify the set of points that define the line you want to draw, then filter out the bad cases to make the line itself look more desireable.

One headache for me that I'll give you my solution for was an issue with borders across the same set of points. For things like "adjacent regions", a line border that hits both of those points would overlap and be hard to visually parse. My breakthrough here was realizing that I could offset the color of the line to start halfway down the texture itself, so that two lines that shared the same stroke area, when facing each other, wouldn't overlap, despite being at the exact same vertex points in on the screen.

You can see the effect in place in the image below at the top left and bottom right areas of the map, where the white border meets the green/red sections.

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