"Sky City" - a one-building city.

YouTube link.

Next year Sky City in Changsha, China, will become the world's tallest building.  But before you mock the idea as national one-upsmanship, consider the following:

This is not a trophy like the Burj Khalifa, a thin high tech spire that isn't even connected to a sewer system. They call it a "pragmatic" building, designed for efficiency, affordability, replicability. They also make a strong case for it being sustainable...

The Sky City concept significantly reduces the per capita use of land, and the CO2 emissions generated getting around... By going up, hundreds of acres of land are saved from being turned into roads and parking lots. By using elevators instead of cars to get to schools, businesses and recreational facilities, thousands of cars are taken off the roads and thousands of hours of commuting time are saved. It makes sense; vertical distances between people are a whole lot shorter than the horizontal, and elevators are about the most energy efficient moving devices made. A resident of Sky City is using 1/100th the average land per person.

It will be built with prefabricated parts on a modular basis, allowing construction to be completed in less than a year.

And it really is a city in and of itself—4,450 apartments, nearly 100,000 square feet of indoor vertical farms, 250 hotel rooms, 92 elevators, 30 foot courtyards for athletics, and a six mile ramp that can be used to walk or run around the entire city...

There's a more distant concern that this may not be the most pleasant way to live; stacked atop one another, separated from open air and nature. Plus, that cookie cutter aesthetic could eventually sap the architectural diversity of the cities of the future, and turn our most notable population hubs into towering Levittowns. 

Or maybe it's exactly what we need, with resource consumption and energy use spiraling out of control. Maybe our best hope is to churn out a host of massive, identical, self-contained Sky Cities to house the booming population—maybe this is the future of how we'll live on a teeming planet.

The most detailed discussion I've found is at Next Big Future, which presents the developers' details about safety, comfort, energy, and sustainability.