When to put new ball into play after HR?

[rwest]

Originally posted by DaveASA/FED
Yes she can appeal the runner missing home until the next pitch. now I would have a dead ball appeal so I hope she just touches home or asks me about touching home to appeal it and doesn't follow her all the way to the dugout!!!

...do you wait until she enters the dug out to give the catcher the ball or allow the appeal. I know the ball is irrelevant during a Dead Ball appeal, but if you give the catcher the ball she might think she can appeal at that point.
So do you wait to avoid confusion? If not and she appeals, do you wait until the player is in DBT before honoring the appeal?