Essentially there is no limit. Even a single channel can handle an infinite number of transactions back and forth.

Remember that you can make lightning transactions peer to peer directly, without anyone else in the network knowing about it.

That means there's virtually no limit, as in the bottleneck would be the people themselves making the transactions in a human timescale.

all of them

Tl;Dr.

My answer is in theory infinite txs.

In reality it's less than that, but some day we will be able to perform more txs on lightning than all other payment processors combined.

How'd I do?

998 of 999.

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