Is it acceptable to write a reference letter for yourself? If a student needs a reference letter for graduate admissions or that sort of thing, some profs will ask the student to write a reference letter for themself before sending it off to the prof for minor edits and finalization. This seems to be a somewhat common practice given that some graduate schools ask for several letters of recommendation even when it is not reasonable for the student to have developed deep connections with that many professors, and that most professors are just too busy to write quality letters for all the students that ask them to.

Is it acceptable to write most of the reference letter and have the prof make minor edits? Do academic institutions frown upon this practice? Would it be considered an academic offense if a student wrote a reference letter for themselves and had a prof sign it?
I don't think this is a grey zone at all. Senior professionals in all domains, not just acadaemia, routinely sign letters that they did not pen:


Directors signing press releases written by communications managers
Vice-chancellors signing letters to government officials written by deputy vice chancellors
Academics submitting journal articles that were written by a co-author, although the research is shared.


It's completely irrelevant who actually put the words together, unless there is a question over the copyright of the text - which there clearly isn't here. All that matters is that the person signing the letter stands by its content and takes responsibility for it.

If you write a reference letter for yourself that is over the top, they won't sign it. No ethical issues here whatsoever.

(I can't answer whether other institutions would frown on the practice for other reasons though.)

EDIT 

Ok, some research.


  Tip: Don’t ask the candidate to write a draft of 
  the letter for you. Most heads of labs say this rarely 
  saves time and sometimes leads to a weaker letter. 
  It is better for the candidate to provide you with 
  all the necessary information, from which you can 
  then pick and choose as you write your letter.


... (and for the applicant)


  You may be asked to write a draft of the 
  letter. As mentioned on page 1, many 
  heads of laboratories say this is not a good 
  idea. However, if you are asked to do it, 
  do it!


http://www.hhmi.org/sites/default/files/Educational%20Materials/Lab%20Management/letter.pdf


  When requesting a letter of recommendation, don't be surprised if your instructor or supervisor hands the forms back to you and says, "Sure, why don't you go ahead and write the first draft yourself, and I'll revise it and sign at the bottom."


http://www.petersons.com/college-search/letter-recommendation-writing-yourself.aspx


  The “draft” that you provide to the recommender to sign shouldn’t be a draft at all – it should be a perfectly polished letter ready to be signed, sealed and delivered.
  Don’t be insulted when your supervisor decides to edit.  They’ll want to apply their own language and voice to your content.
  ...
  I’ve been asked to write lots of letters of recommendations for students, but I’ve never felt strongly enough to throw the responsibility back at someone.  That’s not to say I haven’t managed some phenomenal students; I just haven’t had someone come along who I think is up to the task.  So, when he or she does come along, that person will really be top notch.


http://studentbranding.com/writing-your-own-letter-of-recommendation/


  While the standard practice is for references to write their own recommendation letters, it’s becoming increasingly common for time-strapped individuals to ask you to pen the first draft of a letter yourself.


http://www.vault.com/blog/job-search/how-to-write-your-own-recommendation-letter/


  Question: Is it OK to Write My Own Letter of Recommendation?
  Answer: The only time it is acceptable to write your own letter of recommendation is when the person you requested the letter from asks you to do it. Even then, it is important to be honest in the letter. Don't write anything the other person wouldn't have written. When you have finished, ask the person to look over the letter, verify the information, and sign. You should never forge someone else's signature.


http://businessmajors.about.com/od/recommendationletterfaq/f/WritOwnRecLet.htm

I don't see much (any) evidence of any ethical quandaries in a professor requesting and submitting a letter of recommendation directly from the student. These examples aren't cherry-picked - they're the first few hits that came up when searching for phrases like "own letter of recommendation" or "letter of recommendation myself".

In summary:

Is it acceptable to write most of the reference letter and have the prof make minor edits?

Clearly, yes - if requested to do so.

Do academic institutions frown upon this practice?

No.

Would it be considered an academic offense if a student wrote a reference letter for themselves and had a prof sign it?

Hell no.