how does an 8-bit AVR do 10-bit analog read?
It can do a 10-bit reading quite simply - because the ADC is a 10-bit ADC.  The CPU register size doesn't dictate what it can communicate with, either internally or externally.  The only thing it dictates is how big a number it can cope with at any one time.  Because of this the 10-bit result of the ADC is spread across two registers - 2 bits in the "high" ADC result register, and 8 bits in the "low" ADC result register.