Arduino potentiometer example: what limits the current?
A0 input is high impedance, so very little current is flowing into A0. The value is so small that you can simplify that it flows only from +5V through the potentiometer to GND.

For some applications, when you are measuring high-impedance sources (a source that can deliver very little current) this simplification may not be correct.

You can find more detailed explaination in Atmel application note:

http://www.atmel.com/images/atmel-8456-8-and-32-bit-avr-microcontrollers-avr127-understanding-adc-parameters_application-note.pdf