I stand corrected, it varies by state. I stole this from the Powerball website.
SHARING OF PRIZE; GIFT TAX
Can the Powerball winner designate additional recipients, such as family members? Roger B. via Compuserve.
Prize claims are handled by each state lottery that sells the game. State prize claim rules will vary, but states generally prefer to issue one check and withhold taxes for one person. Note, however, that some state lotteries will issue separate checks and withhold amounts for any number of persons that share in a prize.
Your question seems to suggest that a winner may decide, after winning the jackpot, to share the prize. You should be aware that to avoid the Federal Gift Tax, the persons who are splitting the prize must have agreed to share in the purchase price of the ticket before the win. Most people are not aware of the Gift Tax. When a person dies, the Federal Government collects an Estate Tax (payable by the estate) on the assets of the estate. It would be an easy thing to avoid the Estate Tax by simply giving the property away shortly before death. To close this loophole, the Federal Government also assesses a Gift Tax payable by the person making the gift. If a winner decides to give half of the winnings to a third party, the winner will be charged with a Gift Tax on the half of the prize he or she gives away (at rates up to 55%). In this scenario, the winner is still liable for the income tax on the entire prize.
Players planning to split a prize should be sure to have evidence of that intention so the IRS will not levy an additional tax for making a gift. There are some minimum amounts that can be given away without incurring the Gift Tax, but Powerball winners can afford to give gifts that can quickly reach the maximum Gift Tax percentage.