Best way to integrate composer with CodeIgniter 3.0

[eluser]ivantcholakov[/eluser]

... but that doesn’t integrate CodeIgniter itself in the composer logic (at least system/core files), and that’s the problem I’m trying to solve, ...

I am a little distant to this idea, here is some explanation that I found: https://github.com/EllisLab/CodeIgniter/issues/2262

Because I’m participating to a small open-source project where we compare PHP frameworks between each other over a blog sample, the goal is to provide the composer.json file with the framework package in it, avoiding all the framework system file in the git repo. (It’s better if the user can get all the framework up-to-date core files with a single composer install command)

Sounds like an experiment. Well, the next quotes are related to the link I've given.

Really ? I don’t get this, why including vendor files into the repo whereas the main purpose of composer is to avoid code duplication/storage ?

Why not? I see Composer as a tool for building my project efficiently by code reuse. I don't see Composer as a deployment tool. It is you to use Composer, let the end adopters download the whole your application, don't force them to deal with Composer. Give them everything with just one download.
Also, if your installed Composer packages are part of your source, your IDE's autocomplete feature will respond better.

According to you, what would be the best solution for storing CI-based applications in a repo without storing the whole CI application ?

I don't see such a solution. And I think, I don't need it.