An average minecraft map is what? How far have you traveled, or when was the last time you played? Actually, what version of Minecraft are we discussing here? The free original version, or the current purchasable one?

In the current Minecraft, maps 'infinitely' generate (at one cube = one meter, you can travel more than the equivalent of the surface of the earth by several orders of magnitude before the game engine will start having issues.

An average minecraft 'chunk' is, if I recall correctly. 64x64x128, so 4 of those fit within what you called a map. A server will generate new terrain dynamically (derived from the seed you give the map) as you explore outside of the terrain generated so far. And then keep in RAM terrain within 10 'chunks' of the player (I don't know if that's circular, rectangular, or whatever).

Now, that's the default server and I suspect that stuff is configurable, of course, in most servers.

Of course, if you're talking about the classic Minecraft that's currently free-to-play, I have no clue what map size that thing has, though I do know the 'infinite' maps feature was added after classic Minecraft was detached from the current Minecraft.

- Edit -

Oh, right, OP: Awesome that you got it working. By "work on performance and stuff" how exactly is it performing now? Playable, or just completely lagfest-like?