I'm not sure if you mean what the largest alphanumeric display is or something else like memory.
Each display model is slightly different and I've seen all kinds of sizes.
The standard 2 x 16 is common. 1x16, 4x16, 8x16, 2x40, 4x40, 2x80 are some of the others.
Each of these displays also have memory allocations which are bigger than the characters they can display. So it is possible to store a larger
string in memory and scroll that data in and out of the display