what are the duties of a grand moff?
Dunno, but it’s one step up from a petit moff. 
It’s like a “super governor.” you get governments at planetary, then Governors at the system level, then sector (Moff), and the Grand Moff covers multiple sectors.
Unless there’s only one Grand Moff, and he covers everything… I need to check my books, but I think that after the Empire fell, a bunch of "Grand Moff"s sprung up to try to fill the power vacuum.
BraheSilver, I’m 98.8% sure that you’re entirely correct.
There were multiple Grand Moffs. Tarkin just happened to be one of the more powerful of them (he planned to use his Death Star against the Emperor).
*Who’s the pale wrinkled governor
who’s a sex machine like none other?
TARKIN!
They say that cat Tarkin is one bad Moff…*
sincere apologies to Isaac Hayes