Trust me, your education is like pretty much 95% PAID for by the govt and university. This is really excellent news and best of luck with your family situation!
Not necessarily true in every case. having a zero EFC does not guarantee you a free ride to college as only a handful of schools are both need blind and meet 100% of your demonstrated need giving major scholarship or grant aid. The ones that are are extremely competitive.
Since we now nothing else about you it we would be extremely remiss and irresponsible to suggest that you will get a free ride because you have an EFC of zero being that it is not necessarily true.
If you go to a public university, you will be eligible for Pell, maybe even SEOG, but that does not mean that you will not get loans.
The overwhelming number of colleges in this country are need sensitive or need aware which means your abilty to pay may have an impact on whether or not you are admitted especially if you are not at the top of the applicant pool at that school. (this does nto necessarily help the cause of a student with a zero EFC)
If you attend a school that does not meet 100% of your demonstrated need (gaps) and you have maxed out your resources as far as the amount of $ you can borrow freshman year:
2625 Subsidized stafford loan
4000 Perkins Loan
4000 unsubsidized stafford loan (if your parents get rejected for a PLUS loan)
you could be left without a way to attend school. Read through some of the pages about students who are maxed out on the amount of money they can borrow, parents have no assets and they are still short the amount of money they need to attend school.