Authorizing a new computer

So, for years, my brother and I have shared a music library mostly composed of music burned from our own CDs and some (very few, around 100 or so) from the iTunes store.

All this music is in computer A. Which is also where we download all apps and from where my iPhone gets synched.

Also, we use my iTunes store account to do all this.

Now I want to divvy up the songs we bought from the iTunes Music Store. Some are my brother's and some are mine. Is this possible to do?

Also, I want to do all the updating of my apps and the backing-up of my stuff (from my iPhone) to my computer, B. How do you de-authorize one computer and authorize another?

What I'm most interested in is the splitting up of the songs bought from the iTunes Store. If this can't be done, is it possible to just give the songs away? Since they were bought with my account, they are mine, but most of the songs really belong to my brother, so, can I just transfer them to him?

Thanks.

 

For some reason I thought this was no longer an issue. I thought that Apple now allowed songs to be transferred to another ID.

Ok, but how do you de-authorize the computer you used to back up to (in my case, A)?

Thanks.