An ecumenopolis is a world city or planet-wide city. As a Type 0 civilization progresses towards 1, urban areas and megalopolises would eventually fuse and there could be a single continuous worldwide city as a progression from urbanization, population growth, transport and human networks.
A planet spanning city is only sustainable if there is a sufficient and steady import of food and resources from nearby planets or star systems. This is more plausible for a Type I civilization.
Growth would typically be from the ground up, with the entire surface covered in "sky scrapers." However, if severe climate change happens, desperate measures would have to be taken by to adapt. In that case, underground facilities or "earth scrapers" would be a viable option. These can reach hundreds of meters below the Earth's surface and use new materials and structural techniques. Self-sufficient power generation, production of food and water, fully automated recycling, and heat management are common in these underground facilities. Some facilities are powered by fusion, while others have access to geothermal energy if placed in the appropriate geographical location. Movie theaters, gyms, spas, virtual reality, and other features ensure that occupants are kept stimulated and free of claustrophobia. Most of these underground living areas provide the advantage of being essentially immune to nuclear weapons, as well as various other global threats. As the number of residents in these underground living areas reach into the tens of millions, they will be joined by a network of hyperloop tunnels that connect countries and continents to each other. Many of the design principles in these facilities could be employed on the Moon and Mars or even hollowed-out asteroids.
When planetary cities grow in an unsystematic and unplanned manner beyond normal boundaries, due to increases in population and industry, so that their suburbs merge into the suburbs of neighboring cities, the result is a vast extended metropolis called a sprawl. These megacities can merge and sprawl across a planet. If it goes beyond the planet it is called a swarm where there could be thousands or millions of habitats surrounding a star.
An example of an ecumenopolis is Coruscant.