The way it works at the moment is:
- a fresh wallet only downloads ~ the last week of blocks for the most relevant tx history
- if there already is a block in the local blockchain, the wallet continues syncing from that block onwards which can take some time depending on network availability of the block and the number of blocks required to catch up. So if you wanted to get a local copy of the full chain, you'd need the first block and the wallet would do a complete sync.

Both variations give you the same security and wallet balance though. That's the greatness about the mini-blockchain. You don't need to know all details about old transactions. It's enough to know they exist (as they're still referenced in the proof-chain header) and your current balance from the account tree which is interlinked with that proof chain. Although even the existence is not necessary to get your account balance and can be forgotten.


While writing this, it gave me an idea:
@pallas: do you think it'd be possible for a wallet to sync ONLY blocks that contain my own transactions? So I could get at least a complete tx history for my own wallet? I think that'd be a nice feature to have
I'm thinking about a switch in the wallet options to enable this.