So you click on a tile of the multitile citybuilding with the buy-citybuilding tool.
- You pay for the tile you click on and all tiles south/east of it that belong to the building (=the cost floats in the air)
- You are not considered the owner of the building in it's dialog, unless you buy the north-west corner
- Other players can still delete buildings you own, so long as they use the delete tool on a TILE you didn't buy. That is, to protect a 2x2 building, you'd have to buy all tiles, in sum at 9x the regular buy-building-cost.
(I cannot say whether cities would renovate them)
There is a disconnect - the tool seemingly buys the tile, which in the past would be the whole citybuilding, but isn't anymore. Probably just needs to buy all tiles the building stands on instead.