OK, Let's get a few things clear,
#1 I hope you are aware of the fact, that a registered agent is necessary to incorporate an US LLC.
#2 What do you mean by
privacy? An Anonymous LLC won't save you from a lawsuit. It just keeps ownership information off the SOS website. If you really want to get into the nitty-gritty, research a bit about Holding companies (there are ways - through multi-layered LLCs, involving multiple lawyers), but, nothing stays private/anonymous. You have to disclose the UBO to the bank (if you intend to open a
bank account for the LLC).
#3 Now, coming to your assertion for "Attorney-Client privilege". It's tempting for a law firm to act as a registered agent - but are you aware of why they normally don't go down that road?
Learn whether law firms should act as a registered agent for their clients and the issues to consider, including risks and potential liabilities, non-compliance, ever-changing law enforcement regulations, the potential for ethical breaches, & more.
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