I may be able to offer some information on this topic. I recently returned from a deployment as a MTT leader, and will be returning for a second deployment, again as MTT leader, in a few months. Xenophon generally has the team composition correct, though I never had a comm officer - only the comm chief. Instead the billet is the HSC advisor, and can be filled by pretty much any MOS. It's HSC (Headquarter and Service Company) because the table of organization for all MTTs comes from the army. The overall standard battalion level MTT is an 11 man team following the army T/O. The Marine Corps has added 4 gunner/driver/security Marines to the list to make it 15. On my last deployment I also received 10 additional infantry Marines and a second Corpsman. That was very localized though and a function of the area we were in, the security situation, and the operational status of the Iraqi battalion (in my case they were no longer partnered with a US unit and were operating independently in their own AO). Brigade and Division level MTTs differ somewhat, but follow the same general structure.

The actual MTT assignment are to the T/O advisor positions. I quickly learned that organizing along standard staff functions (S1, S2, S3, etc) was required both for internal MTT functioning and much of the interaction with the Iraqis. I also assigned Marines to company advisor positions. I guess you could say collateral duty, but really it was a second primary duty. Everyone split their time between staff functions/advising and conducting actual combat operations with the companies and the battalion.

As far as assignment to MTTs from what I have seen it is ad hoc and inconsistent. A list of MTT requirement is published and units are assigned to fill certain position and in some cases entire teams. Some people volunteer for team, others are voluntold. The selections occur at all levels (battalion, regt, division). There is no formal nomination or screening process, though there is a general understanding of the attitude and mentality that are required to be successful in this job.

I am in something of a unique situation. Having just returned from my last MTT when my unit was tasked with filling another full team for deployment in a few months. I was given the choice between another MTT tour or a MEF level staff job. I picked the MTT. Fortunately for me most of my previous team then volunteered to come back with me. I was also then given a relatively free hand in filling the remaining spots as well as conducting my own predeployment training. The MEF has made us something of a science project - they want to evaluate how a return team (or team with a good number of encore personnel) prepares and performs. One long term MEF concept has MTTs forming for an extended period and conducting at least two deployments together, though I'm not sure they will ever get to that.