How much do they really take out of a lottery jackpot?

Recently,somone just won the Mega Millions lottery jackpot that was vauled at over $1billion.Of course,taxes will be taken out but exactly how much?One person told me that if you take the lump sum cash option-which most pepole do-they take a certain amount out up front,and thats before you pay state and federal taxes.I was also told that after everythings paid,the winner ends up with about half the jackpot,while another person said you would only end up with about 1/3 of the winnings.What is rhe correct amount?