Very recently I inherited a twinplex and approximately $500,000 from my aunt through
her trust. She lived & died in California andI am located in Tennessee. What is the rate
of taxation on this - approximately how much money do I have to pay in federal tax and
in state tax & to which state(s)?

1. There is no federal tax on inheritances.
2. CA does not have any tax on inheritances
3. For Tennessee check at the state web site.
You may like to read this:
Your U.S. Tax Return: Tax on Inheritances (http://taxipay.blogspot.com/2008/02/tax-on-inheritances.html)