Most mobile games tend to download additional content once the game is downloaded from the Play Store or App Store when it runs for the first time. To exacerbate it, a few games don't specify the amount of data to be downloaded or time taken to download.
1) Asphalt 8 (Gameloft) EditAsphalt 8 build is only 35 Mb if downloaded from Play Store. Once the game is run, it then downloads around 1.2 GB of data in content and additional content. This may be deceiving to some players. Also once the content is downloaded, it takes a significant amount of time to install or apply the downloaded content to the game.
2) Uncharted 4 (Naughty Dog) Edit
This is true for most console games as well. Gone are the days when we just need a disc to play the game. Uncharted 4(PS4) Blu-ray would require you to get the DLC(Downloadable content) before playing the game. Also, some elements of the game content are available only after purchasing a separate add-on.
Halo 5: Guardians had a huge day one patch which caused a furor because it affected people with a slow internet connection. Some gamers had to wait several hours after buying the game before they could even play it while their friends were already playing it.
4) Plants vs. Zombies 2: Its About Time Edit
Plants vs. Zombies 2, exhibits this behaviour of downloading files post initial install as well. These downloads deal mostly with updates to the app's content. By applying this approach, the developer has bypassed the need to release a formal update through the various mobile app stores. Instead the app automatically updates itself when new content is uploaded. While this might be convenient for the developer, the player often must wait for the said update to be applied before playing the game. Further, since this is a mobile game, often this download might take much longer or fail to complete, owing to cellular network issues.
In Hearthstone, specifically for mobile, they have large downloads that will automatically download without asking. These can sometimes be upwards of 2 Gigabytes of data, and one must go in and manually change the option to not download it automatically. Also, it asks to download, but will not tell the player how much the download will be. This can cause overages for players, which turns people off from the game.