So in light of what's been going on lately with Coinbase, I've been looking at ways of reducing my paper trail. I thought that simply sending my btc to an external, anonymous wallet would be enough but apparently that can still be traced really easily through the blockchain. I'd prefer not to have to use a tumbler with the related fees, so I've been looking at an HD wallet like mycelium or breadwallet. I don't really know that much about how bitcoin works, so could someone explain what an HD wallet is to me? How much more anonymous is it compared to a regular wallet from, say, blockchain.info?
I use Electrum was in a HD wallet, which I assume you are saying a deterministic wallet? With these types of wallets, when the wallet is created, you are given a random set of words. Keep these words safe. You can completely regenerate your wallet from these words - it'll rebuild it all without having to do backups or what not. Restoring these wallets is quite easy but you have to have that original seed/phrase/set of words given to you at the beginning.
Also, Electrum, as I guess with other HD wallets, will generate a series of receiving addresses. Basically, I'll do one transaction per receiving address. I think you'll start off with 5 receiving addresses (configurable) and as you use these receiving addresses, Electrum will generate new ones for you. You can generate as many as you need.
I actually switched to Electrum b/c of the whole Coinbase debacle as well. So far I love it. But this is not really teh same as a tumbler, so Electrum doesn't replace that functionality. The taint isn't broken so if Coinbase is looking down the blockchain and say you transfer funds to one of the blacklisted addresses, I think they will see that down the blockchain. But I guess you'd have plausible deniability to a degree in that there is a buffer b/w you and whereever you send the coin if you use some other wallet in the middle, but this would be true of any wallet in the middle not tied to your identity.
So what Electrum will do when you send money, it'll start spending from the oldest receiving address and keep going through address until the send amount is covered. Obviously, almost certainly, you will have "change" left over (adding up all the wallets that electrum is using to send the coin), it'll send the change to yet a new bitcoin address generated by Electrum wallet. Its pretty cool how it works, I like it. Basically, you keep generating new addresses as needed, using each one once. BUT, this doesn't replace what a tumbler does. Anyone could go down the blockchain, see your transaction from say Coinbase to electrum to a DNM or whatever.