This follows the rules for capturing standards, with the following exceptions.
If the battle standard bearer is fighting on his own, the enemy may capture the battle standard by either killing the bearer in close combat or by breaking him and pursuing. The standard is then captured and held as a trophy exactly like unit banners.
If the battle standard bearer has joined a unit and the unit breaks from combat and flees, he will flee with the unit and lose the standard. In this case, the enemy may capture the battle standard (together with the unit's standard if it has one) by pursuing, as normal. If this happens, replace the bearer model with one that does not have the banner or otherwise mark the model to represent that it does not carry the banner any more.
If the battle standard bearer has joined a unit and he is slain in close combat and his unit breaks and flees in the very same turn, the battle standard can be captured as described above.
If the battle standard bearer has joined a unit and is slain in close combat, but his unit does not break in the same turn, the battle standard is simply removed as a casualty and cannot be captured.