none of the squirrels I feed are fat...I feed them sunflower seeds and if it's really cold some homemade pancakes that are dried out like a huge cookie or cornbread
I encounter squirrels in the city park near where I work. They are so tame because people feed them, and even a little aggressive (one jumped on my leg once!). Out of all the lunch food I have tossed at them, what they like the most is grapes. They go nuts for grapes! They will not eat a lot of stuff, though. The sparrows and pigeons will eat just about anything. Even each other, most likely. They eat chicken!