Well if your are talking about PCH, they will more than likely withhold the required taxes, Does not mean you will not owe additional taxes, they have no idea what your other income might be.
But generally in prize situations they withhold more than the applicable rates. See Circular E for withholding requirements.
If by chance you were to receive income of $5000 a week that they didn't withhold the taxes from; then it is your responsibility to make those payments by estimated payments.
They'd withhold some taxes from every check. At the end of the year, you'd fill out a tax return, showing an annual income of $260,000. You'd pay or get a refund, depending on how much had been withheld, just as you do with any income of any amount.