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Extenders are components that add, and manage for, properties to other components.
Since it's impossible to add properties to another class or object, the properties added by an extender only look like properties in the designer. At runtime they are simple Set/Get methods on the extender itself.
Some extender are not even a separate component. For example, the TableLayoutPanel, FlexLayoutPanel and FlowLayoutPanel are all extenders and add properties to their children. This feature is extremely powerful in a web system, when you drop a control inside a FlexLayoutPanel, that control "gains" new properties such as FillWeight, AlignX, AlignY, etc. These are properties that make sense only when the target control is inside a FlexLayoutPanel.
You can add multiple instances of the same extender. If you add two (or 10) Animation extenders you will be able to define multiple animations for each control in response to different events.
Return true if the extender wants to extend the target object. There isn't anything more to it and there Microsoft documentation and examples are quite exhaustive.