re-hydrate dried and salted cod with water and milk I usually re-hydrate and desalinate dried and salted cod with water, changing the water several times during 48 -72 hours, keeping the fish refrigerated during the process.

dried, salted cod pieces
Lately I've read people use water and milk for the soaking. As I didn't find any information about that technique I'm wondering what is the benefit of adding milk? What is the change in the fish itself, if we use milk to soak it?
Normally I poach the fish in milk as a last stage of preparation, especially if I'm making brandade.  The milk, in that case, adds creamyness to the fish. both making up for some of its residual dryness as well as helping mask the salty taste.  However, that's after the fish is soaked in water for 24-48 hours.  A 1-hour poach in milk is also my way of &quot;emergency quick soaking&quot; cod.
Presumably soaking it in milk would be to achieve the same effect, without poaching it.  Salted cod has almost no fat, so the milk bath would be adding some much-needed fat to it.