What would happen to housing markets if legislation eliminated property taxes?

Realistically it can't happen, and even in the hypothetical, prices would likely rise rather than fall. Property taxes are a core funding source for schools, roads, and local services, and states and municipalities would have no way to operate without replacing that revenue. So treat this as a thought experiment, and never a policy to plan around. Run the hypothetical anyway and the mechanics are instructive. Buyers largely shop by monthly payment, and that payment tends to absorb roughly a set share of household income. Strip property taxes out of the payment and you've freed up room in the same budget, and history says buyers bid that room into a higher purchase price rather than pocketing it. The monthly cost of owning drifts back toward where it was, with a bigger loan balance underneath it. The tax line vanishes and the price line climbs to fill the gap. There's a fairness wrinkle too. A change like that mostly rewards people who already own, whose asset just got more valuable, while doing little for someone still trying to buy in. The durable lesson is the part that actually helps you: lower carrying costs get capitalized into price. That's the same reason falling rates tend to push prices up instead of making homes cheaper to own.