General 2k texture support

Is it safe to target 2k textures by and large for reasonably modern (few years old) hardware (mobile and PC), or is 1k still the only universal texture dimension? What happens on a device that can’t support 2k textures? Just fails?

I don’t know exactly but I think a year or two ago iOs devices stopped supporting less than 2k because a version of OpenGL ES 2 or something made it mandatory? I might have my facts wrong. I think 1k is a really old standard. You can check the unity webplayer stats etc to see what the maximum texture size is.