I bought from my dad, after my mom passed. He wanted to downsize, we wanted a home in a neighborhood with good schools. It was a win-win.
We hired an escrow/title company and got a regular purchase mortgage. My dad had paid off the house- but if he’d still had a mortgage, that would have been handled at closing like any other home resale closing.
If your parents have owned the house for a while AND are not rolling their lower tax rate into a downsized home, you can continue their lower, Prop 13, tax rate.
But it’s an either/or situation. My dad was downsizing, and wanted to take his tax rate with him as an over 55 year old. But we wanted to keep the tax rate on the home we were buying from him.