Say I hit the Mega-Millions for a huge sum of money. I’m a smart guy, so before I show up at the lottery agency I first go to see a lawyer, accountant, financial adviser, etc. After I sign the forms and the taxes are taken out, I choose to take a lump-sum payment of $200 million.
What happens then? Doe the state, or lottery agency, simply dump $200 million into my bank account?
(Unfortunately, I don’t need a fast answer.) 
Don’t they just hand you a check? A huge big one for show but also an actual regular sized one that you hand to your financial team to diversify for you.
In CA I believe they actually cut you a physical check for the first payment ( only payment if you take a lump sum ) at any of their designated lottery offices and will provide a security guard to accompany you to a local bank. After that if you have an annuity, you can designate an account for it to be deposited into. But for some reason that first one is done with real paper.
Sadly I don’t have first hand knowledge of this either, but this is according to the official handbook, which I checked a couple of years ago out of curiosity.
LOL I think if I won one of the huge ones, my credit union [which is reasonably small] would first plotz then stroke out from shock as that would probably double their [tiny] worth. 
My local bank branch is in a grocery store. I imagine if I showed up with a check for that much money, the two people working there at any given time would have strokes. It’d be like some odd Doctor Who episode where he hits the robots with the sonic screwdriver and they start jerking around before keeling over.
Oh, and NO, if you won $200 million cash option, you don’t get $200 million. There’s these pesky little things called taxes that they take out first. At least in the USA.
No, my OP specified that it was $200 million after taxes.
According to the Powerball FAQ they can direct deposit into your bank account if you bring them your info, although if you show up the day after the drawing, you may have to wait a bit.
I’ve read that here in the U.K., the National Lottery has a team of people to advise you on your new wealth.