Would get divided based on your share.

Property taxes discourage building. Empty land is really cheap, property tax wise. Once you build on the land, property taxes go way up. This discourages you from building on the land.

Land value tax is the opposite. The tax you pay is based on how much the land is worth, based on its location and supply/demand. An empty lot in NYC would cost the same in LVT as if it had a big apartment full of renters. This makes it very expensive to hold on to unless you’re going to build on it.

The same applies for improvement. If you own a plot with a single family house on it in an area where demand is skyrocketing, your LVT is going to shoot up along with it. This encourages you to either tear it down to build apartments or sell it to someone who will.

The really interesting part about LVT is that it paradoxically makes housing more affordable. One of the biggest problems with the current property tax system is that people’s taxes don’t go up when the value of their property increases. This leads to little old ladies sitting on multi million dollar homes and paying almost no taxes at all in places like the Bay Area. Land Value Tax would force tons of those houses onto the market, causing prices to go down due to increased supply. Truly expensive areas would also have to have apartments built to cover the tax.

The other nice thing about LVT is that landlords can’t pass it on by raising rent. Since the cost of rent in the area directly determines the value of the land, rent increases just turn into tax increases. At some point landlords have to stop increasing rent otherwise everyone would move out and then they couldn’t afford the taxes, so this leads to an equilibrium.

The only thing left to solve in this system is to make sure taxes are used to benefit regular people and not wasted.

Empty housing is empty land. It just has a house on it. And there are times and places where landowners will spend decades sitting on infill waiting for land values to go up. Additionally, land that could be developed into high density housing but is being held at low density at the behest of the area's politically connected residents, is kind of like "empty" land. It isn't a binary.