* The depth of their relationship with the student: A TA who has worked closely with a student, grading their work, observing their participation in class, and having meaningful interactions, can write a much stronger letter than one who only had superficial contact.
* The TA's familiarity with the applicant's skills and abilities: The letter should demonstrate a clear understanding of the applicant's strengths and weaknesses. A TA who only graded assignments might not have a comprehensive picture of the student's overall capabilities.
* The institution's policies: Some institutions might have guidelines about who can write letters of recommendation, potentially restricting TAs from doing so, particularly for significant applications like graduate school or prestigious scholarships.
* The TA's writing skills and ability to articulate the student's potential: A well-written letter is crucial. A poorly written or vague letter can hurt the applicant's chances.
In short, a TA *can* write a letter, but it's generally better if the applicant also seeks recommendations from professors who have a more comprehensive understanding of their academic abilities and potential. A TA's letter can be a valuable *supplement*, but rarely should it be the sole recommendation, especially for high-stakes applications.