:: You still own it but they control it ::
No. Without pressing your 4th Amendment rights, you give up ownership of the property in question...period...fait accompli.
Regulation is a “taking” but we have just given up on that angle and the courts have settled on such. Roberts said [par], It is not the requirement of the SCOTUS to protect the citizens from their elective choices.
Let me translate: You elected the asshole...tough shit!
Well as long as you follow government rules you will own the firearm. That's the problem. You will purchase the weapon, pay for it and it will be registered in your name. The government will not purchase the gun or be the registered owner. The feds are not going to buy your weapons for you. If someone steals the gun and commits a crime with it the government won't go after the government itself. No it will go after you. You are the owner. If you don't follow their rules they will then take / steal your gun.
There are other items of property where the government will seize / control the property if you don't follow their rules. If you are busted with drugs they will seize your automobile. You must maintain a license plate if you want to drive it. They don't own your car. But they regulate it and control it.
What is different however, is there is no constitutional amendment that says your right to possess an automobile will not be infringed. That's the difference. They have no right to make you register a gun. The fascists will dictate and control under what circumstances you are allowed to retain your property.
Guns is just one item. They will do the same thing on houses next. They won't outright take the house. They will establish some absurd federal property tax and when you don't pay ... then they will take it. They are sneaky like that. This is not communism where the government owns everything ... it is fascism where the government controls everything