Yes, they do, along with other evidence of achievement such as SAT or ACT scores, a portfolio of accomplishments, projects, and curriculum studied, and in some cases an interview with the student, along with a "Statement of Purpose," which tells the university who you are and what you intend to do with your college degree. This is much the same as it is for any graduating senior in any educational setting. And your student is eligible for Financial Aid too. The Home-School Legal Defense Association has a detailed list of colleges and Universities that accept homeschoolers.