Only the portion that is being remodeled or added to the existing home is assessed. The final assessment resulting from the new construction is then added onto the factor base year value.
They only assess the changes.
It makes sense.
Otherwise if you're paying $1000 per year in property taxes (instead of $12,000) and you put new countertops in, you'd be hit with a massive reassessment.
They even give an example in their fact sheet[2]. Adding two bedrooms would add $200,000 to your base assessment which is set by Prop 13.
Countertops wouldn't trigger reassessment. It has to be electrical, plumbing, or structural changes (e.g, changing the size of a window or door entry).
Kitchen - structural changes, upgrading of plumbing and/or electrical systems, changing the floor plan, increasing the size, replacing cabinets, countertops, flooring or built-in appliances with upgraded material and finishes
Replacing old countertops with same material, but new, would trigger an assessment, but upgrading them would.
You will get re-assessed even if you left the frame (or one wall standing). And new construction is reassessed. And even under prop 13, tax can increase 2% / year.
Prop 13 is not why California doesn't have enough housing. This is a lie propagated by teachers unions who flood internet forums with falsehoods.
California's problem is there are hundreds and hundreds of little "cities" each with their own restrictive zoning laws.
They need the state to overrule zoning laws and allow denser housing.
These local cities also cut "sweetheart deals" for companies and give them property tax breaks. So Apple or Facebook or anyone building a new campus pays bargain rates -- not because of Prop 13, but because the local cities have the ability to negotiate tax rates for these companies to encourage them to move in.