How to recreate dynamically added controls on postback without having them appear in duplicate?

[keithb]

I posted this question earlier with an unclear predicate. Let me give it
another shot:

I have found that unless I re-create dynamically added controls on every
postback, I am unable to access them programatically. When I do re-create
them on postback, I can access them programmatically; however, the controls
appear on my webpage in uplate. How can I recreate the controls on postback
without having them appear in duplicate?

Thanks,

Keith