If a California resident has a second in say Arizona can they just move their weapons to the second home? Do you need to notify the Ca DOJ? They would still own the firearms but they would not be in their possession in California.

Stuff is currently registered.

Move your stuff, no need to tell anyone.
Probably better to keep it registered in Kalif as long as there is the possibility of ever bringing it back into this state, even temporarily.

Which State's plates will be on your car?  Which State driver's license will you carry in your wallet?

It's very complicated.  They even passed a specific new CA law to prevent double residents from moving guns.  The other problem is: the definition of "resident" is complex, and can be different for different aspects of the law.  For example taxes, building permits, guns, driver's license, car registration, and so on.  If you have specific questions, you probably need to consult a real lawyer; multi-state residency is too hard for amateur internet lawyers.

Thank-You for all the answers.

Yes, residency is tricky.  Which residence is listed as your primary residence on your income taxes?  Primary residence is important.  Simply owning a home in each of two different States does not define or re-define your residency or allow you to selectively claim various residencies to avoid complying with laws you don't like.

Agree with trollslayer.  And what I didn't make clear enough in my post: residency for one purpose does not imply residency for another purpose.  There are various things that look at residency (taxes, owning property, and driver's license are the big ones that most people see), but they don't mean that you are also a resident for gun law purposes, or for things like reduced college tuition.  You can even have different residency rules for federal and state gun law.

Sure.  There is no restriction on taking your own firearms out of state and bringing them back.  Of course, if you took out a firearm that should have been registered in Ca. as an assault weapon, you wouldn't be able to bring it back (not that you weren't already in a problem situation if you had it unregistered at home).

You can transport registered assault weapons out and back as long as they are transported in compliance with the laws on transporting assault weapons.

Note that legally removing the AW from the state is one of the approved methods of disposal, or if inherited, desiring to transfer, etc.

https://oag.ca.gov/firearms/regagunfaqs#8

I'm pretty sure one generally can only be a legal resident in one place at a time, that governs federal and state purchase laws, CCWs, etc.  If "moving" into Ca., there are registration requirements for new residents, can't import AWs, etc.  IIRC, the idea that you can take and leave firearms on out of state property that you own (perhaps rental is OK as well) is covered by federal law, too, like you can't leave them with another person (on their property) without dealing with time limtis, transfers, etc.