I've done some research since I first posted, and my understanding
is as follows ...
1) The Feds will loan you money according to rules very similar to undergrad, except that graduate students are assumed independent.
Subsidized Federal loans are limited to your expected need, or the subsidized loan cap ($8500/yr), whichever is lower. Expected need is (TCA - EFC), where TCA is the total cost of attendance (tuition + living exp) and EFC is your expected contribution (50% of previous year's after-tax income plus 20% of current assets). [N.B. 50% of NET income, not GROSS as previously suggested.]
Even if your EFC is 100% of the TCA, you can still get unsubsidized Federal loans up to the combined Federal cap (total subsidized+unsubsidized limited to $20500/yr).
2) Law schools may have their own "institutional methodology" which they use to determine if they will loan/grant you additional money. They may inquire about your parents' income/assets even if you can prove you are independent.
3) You can borrow the difference up to the TCA using Grad PLUS and/or private loans, assuming you are creditworthy.
Say tuition is $30k and the law school officially estimates living expenses at $20k, for a TCA of $50k/yr. If you made $70k after taxes the year before, and you have $50k in assets, then your EFC is
($70k * 50%) + ($50k * 20%) = $35k + $10k = $45k
Your expected need is $5k, which you can borrow subsidized. You can also take another $15.5k in unsubsidized loans to bring your total Federal loans to $20.5k.
If you need more money (and you will), you can borrow up to $29.5k from a private lender to bring your total up to the school's $50k official TCA estimate. Private lenders may or may not be allowed to lend you more than that, so hopefully the school's $50k total (based on $20k living expenses) is realistic, or you'll be dipping into your savings.