Internal transfers
Internal transfers are when a student transfers from one of Columbia's schools to another school also at Columbia.
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Between CC and SEAS
Students rarely transfer from SEAS to CC, but it's nevertheless possible. To apply for this transfer, a candidate must fill out the same application as transfer candidates from other schools, but the application fee is waived. Supposedly, there is a special internal transfer pool, so internal candidates are not lumped into the application pool from other schools (of which ~5% is accepted). No data is available on how many students successfully attempt to transfer between SEAS and CC per year, but supposedly there were 11 successful candidates in 2003-2004.
As of April 9, 2010, there have been reports that at least 4 students (1 SEAS, 3 CC) from the class of 2013 have successfully transferred.
Also, various sources claim that transfer admission decisions for the 2010-2011 year are to be released on April 23. However, successful internal transfer students have been informed on April 5 and are required to reply to the Office of Undergraduate Admissions by April 12, 2010.
Between CC/SEAS and GS
If you drop out and aren't allowed back as a CC/SEAS student, you may be able to return via GS. There is apparently a procedure for transferring from GS to CC/SEAS but there are no documented cases of this occurring.
Between CC/SEAS and Barnard
At least one student in the class of 2009 transferred from CC to Barnard for the '07-'08 school year.