How big of an LED screen can you build?
We can build as big of a LED video wall as can be dreamed up, given enough structure and electrical power support. Those are the two main factors that start limiting size if you would have an unlimited budget. With every square meter of screen area added, you need a bit more electrical power. At some point, you would be drawing so much that you would require more dedicated power to be brought in or constructed. The other obvious factor limiting size would be the support structure and weight balancing. And the third and probably most obvious factor limiting size is obviously the budget.
There are other considerations too, such as current hardware and software limitations regarding content pixel count, etc… To be frank, given the right set of circumstances we can build really, really big screens.