Mark Kohler explains LLC registration in another state. You need a registered agent in that state, but your business address can be anywhere. He warns against using a home address and recommends a virtual mailbox service for privacy.
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When you register in another state, there's two things they're going to ask for: this registered agent who is going to in that state receive notice if someone's pissed off. Second pro tip: when you're registering in that state, they're going to need the company address. Now, the company address does not have to be in that state; only the registered agent does. So again, you can use your company address in Arizona if you're setting up an LLC in Georgia with your rental property. But just don't use your home address, please. Try to use an innocuous address. We have a virtual mailbox service where our law firm will be your address and they got to go through us to find out who the hell you are. So, that privacy can add a lot of benefits too.