After Effects render constraints for .mov with h.264 codec maximum dimensions 2000px x 2000px?

No, not at all. It's inherent in the compression format and AE can't do what QT can't do, anyway. All MPEG derivatives are built ariound specific limits that can't be circumvented and while some of that can be made less severe by picking different profile levels, there are some hard limits still... You need to think of something else.

Mylenium

Can you describe what you're trying to accomplish?  Looking at the dimensions, it appears to be a multiscreen display. 

In such cases, you must always, Always, ALWAYS know your delivery specifications before you begin work: media container, dimensions, frame rate, and codec.  If you don't, you're probably headed for trouble.

I would consider asking this question not here, but on a different web site and a different forum: the Live & Stage Events forum of the Creative COW.  The people there deal with similar situations all the time, and they know the diagnostic questions to ask when someone produces video for multiscreen.

Thanks for being forthcoming with the specs.  I suspect you'll need to use a third-party compression application to make the necessary file(s). 

I don't know if Adobe Media Encoder can do it (you can try it), so you may have to investigate a Telestream product, Apple Compressor if you're on a Mac, or Sorenson Squeeze.  Render lossless out of AE, and use any of them to make the final delivery files.

When Adobe put dimension restraints on certain file types, I suspect the engineers had efficient compression in mind more than the need to deliver out-of-the-ordinary dimensions.

I am working on a project with this exact same spec requirements with this exact same problem.

I honestly think the specs requirements are incorrect. I've seen a few of these forms, the spec part is always pretty much the same. I'm hoping it's more of a suggestion than a rule. I'm about to deliver an MP4 with the codec, dimensions and file size they require.

I'll try to follow up and let you know how it turns out. If I don't follow up, either everything was fine and I forgot about it, or they killed me and I'm dead.

yes you can make a .mov at this size, you are just going about it the wrong way.

i personally never render to h264 out of AE.

a better workflow is to render to an imtermediate format like prores and then do the compression after.

some tools put restrictions on making h264 files that are in .mp4 containers because there are guidelines that are supposed to be followed

anyways... render out to prores. drop in to mpeg streamclip and export to h264. it works.

i havent tried it in AME but that would probable work as well, just dont try a .mp4

No, AME won't export a quicktime container for H.264 with more than 2000 px.

Thanks Danny, the workaround was successful.

First I rendered the Ae comp to image sequence (as I don't need audio for outdoor LED)

then I've used QT pro to convert the sequence to .mov file.

Thanks all.