How much does the steroid spread in an epidural steroid injection?

Just like milk : Coating a glass or a spill spreading on a table but motion and gravity also play a role. There is a potential space or epidural space where this injection is delivered, this can spread locally once in place through the pressure of the injection as well as by gravity effect and motion of the tissues.

Not far: Typically, if a patient is positioned correctly, there is spread only over a few vertebral levels as this is typically a precise localized injection.

Hard to say: Depends on the type of epidural injection done (caudal, inter laminar vs transforaminal approaches), also on how much volume is being injected as well. As a rule of thumb most injections stay at the level injected, if using more volume you can get spread 1-2 levels above & below the level injected.