As I understand it, while you can give/leave-upon-death up to $5,000,000 in a lifetime before being hit with the gift tax, you can actually only give $14k a year (this is the current 2016 annual exclusion) to any individual other than your spouse (no taxation between spouses) before you get hit with additional taxes (outside of gifts directly for medical or educational expenses). So, one way to step aside from this is, "Look, folks, I'm not giving any more money to the IRS because you want to get paid."
https://www.irs.gov/businesses/small-businesses-self-employed/frequently-asked-questions-on-gift-taxes
In my own case, if I'd hit the $2M Holiday Gifts and had just shy of $1M cash when it was all done, I'd only have about half that left after covering the costs of ensuring my own future (zero debt, paid for housing, transportation, medical/educational costs of my own, etc). That's before even getting into putting money away to supplement living expenses for as long as possible. I'd certainly pay off what my folks have left on their house (which isn't much now after decades living in it) and (just as you mentioned) pay off cars for my brothers, along with starting a modest college fund for my niece (particularly since I don't ever want kids myself), but after that my family members would get some fat envelopes of carrying-around money at New Years (a few grand-ish each, probably). I certainly wouldn't be cutting $100k checks (sorry folks, that kinda cash just isn't there to go around). And if anyone pushed they'd get one very angry lecture from me about how it was me extending my neck playing these bloody games, and if they want to get paid they can spend years and thousands of dollars trying too.
An exception might be if they were actively involved in you getting the win, but since that's not the case here, it's not worth speculating about.
There's another issue with handing out money to family (especially those who weren't involved in you getting that money in the first place): extended family. Once one family member tells another... ...you get the idea. For me, I'd be like, "What uncles? What cousins? I don't know those people." But, I'm a monster. :)
On a much larger win, say, on the crazy chance a one-off $10M Fortune ticket actually hit for $10M, I'd set up a trust to claim it and set my family members up with percentages of the trust as I see fit (it would be enough money to reason them taking 30-40% collectively). But, it really would require hitting something that large.