<p>Grad school admissions don’t depend on prestige. They depend on the student and the credentials you present. Academic preparation, what research, what your letters say about your research potential. As long as you are from a respectable school it doesn’t matter about prestige. Now if your department produces very good candidates in the area you are applying to, that will be known and appreciated and very helpful. If you have research and a letter from someone known in the field or a subarea, that is a big plus. But not necessary.</p>