Why do laptops need larger transformers than mobile phones?
Laptops and cell phone both use switching power supplies so the adapters are not simple transformers. 

For a given technology there is a relationship between power capability (measured in watts) and size (volume, specifically). So a cellphone that needs 2.1A at 5V (about 10W) can use an AC adapter that is much smaller and lighter than that for a notebook computer that requires 19V at 4.62A (about 90W).