You can hide ownership in real estate using land trusts in states that support them. You can fund an LLC with a vehicle to hide ownership of the vehicle by VIN or plate search. In both cases, startup costs are a few hundred dollars, and ~$100-200/year upkeep per asset.
Trusts in general are simply good estate planning compared to probate costs, at least on the topic of real estate holdings and titling.
New Mexico has fairly decent LLC privacy and you don't have to pay an annual fee to upkeep your LLC at all. Just need to have a registered agent, which can be had for under 100/year.