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I have a custom control that I'm adding to a Placeholder, when I click on a
button within my control, it should fire an event handler. This works fine
if I simply add the control to a page, but if I add the control dynamically
to a placeholder, the event handlers don't get called.

Are you adding the control in page init or page load? You have to add
it during one of those two phases.

Post code if ur question is still not answered.