What constitutes a completed city. My son and I have been playing for a little while, and we can't agree if a city is complete when it has attached cities sections which aren't.
A city in Carcassonne is completed when their are no places you can possibly add any additional tiles to grow that city.
Three Cities, A, B, & C. Three Tiles that can be laid down (1,2, & 3) in the Green Square..
So in this first picture; only city "B" is completed (3 tiles); as you cannot add any more tiles to that specific city; city A & C are incomplete as you can put at least one more tile on both of those cities (Green Square).
In this picture you will see if we use Tile #1 in the green square; we are actually merging Cities A & C; making a single city of 7 tiles. City B is unchanged and is still considered completed.
In this picture we played tile #2, it completed both City A (4 tiles) and City C (4 tiles). None of these cities can grow anymore so they are ALL considered completed.
Using tile #3, will actually keep both City A & C open as they both have at least ONE place to add an additional tile.
Also depending on what additional add-ons you have added to your base game, you could also play a tile like
that closes city C and leave city A open.
A city is completed when it has a fully connected border and the area within that border is completely filled. If the tiles that form the city have other city pieces, then as long as those pieces aren't part of the city then the city is still completed.
One way to think of it is to imagine that you're working in MS Paint. If you drew the borders of the city with the line tool, then clicked inside the city with the fill tool, then that fill shows the extent of the city (and if that fill would start spilling out into other regions, then that means the city isn't completed.