PhD/Grad School funding and Admission Question

[eesj]

When a university is offering funding to a student what does this cover?

Does this simply cover the cost of living expenses, and tuition? If my employer is currently offering to pay for my tuition to attend a PhD program, will this have any influence on the admissions committee?

[eesj]

I plan on applying to the PhD EE program at Stanford. My employer will most likely pay for all the tuition costs, books etc. The only thing they will not pay (at the moment) is things like fabrication costs (things dealing with the research).