Mostly schools’ financial aid administrations.
Form 8821 (pdf).
Do I have to file this form concurrently with my tax returns for the IRS to process it, or can I do it subsequently as well? Moreover, if I make the time period range from present to, say, 5 years from now, will whomever I grant access be able to access my 2012, 2013, 2014 tax returns, or only my 2010 tax returns for the next 5 years?
You don’t have to file it together with the tax return. If you indicate that the authorization is for 2010, then the form is valid for that year unless/until you revoke it. You can include future tax periods, subject to the following limitation.
Out of curiosity, couldn’t you just provide copies of your tax returns to the financial aid administration yourself?
Sure, but you might have doctored them. I presume this is why they would prefer to get them directly from the IRS. I presume the same logic explains why the Admissions Department of these schools want to get your transcript directly from the school, and not for the student to send it in.
Fair enough. In that case, I suggest using Form 4506 or Form 4506-T, and indicating that the tax return should be mailed to a third party.