Components and their instances (Objects) have nothing to do with Forms. Components are Global and need only to be added once to a project.
Objects belong to modules, not Forms, and you can see the Objects belonging to each module in the Project Explorer window on the right in the IDE.
However despite belonging to a module all Objects are visible globally and can be used in any other module by prefixing their name with the name of the module to which they belong. e.g. Main.SomeObject. To use them in the module to which they belong you do not need the module name prefix