Are relay logs necessary for replication?
Replication does require relay logs. IF you have a replicating slave then it does use relay logs, and you have not disabled them. Please check the following:

SHOW SLAVE STATUS \G


Do you have Slave_IO_Running: Yes? Then your replication seems to be running. Please look for the Relay_Log_File column - what does it say? It should point out the current relay log file.

Look for this file. It should be by default on your @@datadir. Is it there? There's your replication relay logs.

You say you've disabled the relay logs -- I suggest you haven't (I don't even recall there's a way to disable the relay logs). How in your opinion have you disabled the relay logs?