Real Estate taxes are usually always based on the appraised value of the home that the tax appraiser sets when they visit your home to assess the value of your home and any improvements that might have been made.
Although I've known a few people have their Real Estate taxes go up after they bought the home outright and then had the deed changed to their name and the taxes were then set at the purchase price of the home for 3 years until the house got reassessed and then the Real Estate Taxes went down to what they were before.