In California, your value is nominally bound to the actual value (i.e. it can be reassessed at any time). However, given that prices go up faster than the limits on raising assessed value in Proposition 13, in reality the tax is effectively "Sales price plus MIN(Inflation, 2%) per year"
My current house was being taxed at a value of 1/8 of what I paid for it.
If you remodel, you are suspose to have your property reassessed.