It will shrink and eventually be eclipsed by digital, but I‘d bet The New York Times will be printing and distributing newspapers for the rest of my life. At least the next 30+ years.
The random local small-town penny savers and second (and third) tier newspapers will go the way of the dodo, but The New York Times will be the last print pub to turn the lights out.
There will always be people (myself included) who are digital-literature and yet prefer reading on paper. I gladly pay a premium to get the newspaper thrown in my driveway on weekends. When I’m vacation, I look forward to walking down to the general store in the morning and coming home with a bag full of bagels and an armful of papers.
Print books aren’t going away, and neither are print newspapers.