More channels just add more linked addresses per channel.
This is a wrong understanding. Each channel is independent from another and they are not linked. When you route a payment from one channel to another, the blockchain never sees that.
I didn't mean that addresses of multiple channels are all linked together, I should've stated this more accurately.
The idea to mix UTXOs - if you were not to use a submarine swap provider - would be:
1) For each UTXO open one channel. This channel will be between the device holding this UTXO and one 'collector node' such as one another computer or a mobile wallet.
2) Send all funds to the secondary LN wallet through Lightning (non traceable).
2a) It will receive the payments through different off-chain routes and end up with one channel with a high balance.
2b) The 'sender channels' will be empty and can be closed. The blockchain just sees one transaction each, crediting some hub or intermediary on one random route between sender and receiver nodes with the full amount.
3) By then closing the phone wallet's single channel, it will be a single on-chain transaction crediting the phone wallet's address a certain amount that is roughly equal to whatever you locked up on-chain in all the different LN channels earlier. But there won't be any way to tell for certain, other than maybe the similar amount.
I think I got this part in my understanding earlier, too, but didn't express it. OK, I get the idea of the procedure which would be pretty difficult to follow with some confidence.
a) You can't necessarily link the UTXOs for the multiple channels, unless you made some major privacy errors in front which linked all UTXOs to one entity.
b) When funds are on LN they become somewhat stealth in terms of visability of third parties, i.e. Bitcoin flow analysts or whoever is interested to watch.
c) You can put an arbitrary delay of moving funds, closing the channels and cashing out from the destination LN wallet which should make linking the coin flow very hard. Time is not necessarily linked, there might only be a clue by similar amounts (minus on-chain and LN forwarding fees). You could even cash out the destination LN wallet before you close the initial sending channels.
d) Usage of loop-out or boltz.exchange would allow to break apart the total of transported funds which would make linking the coins even more difficult if not nealy impossible.
OK, thanks for en
Lighting.