Styling Disappears when using wrapper or &tmpl=component

I have noticed that the template's styling disappears when i use a wrapper or &tmpl=component.

How can this be fixed?

Thanks

I was also wondering if this is possible. Basically I'm wanting to iframe a component from one Joomla website into another Joomla website. The content shows fine in the iframe but it loses the original site's template styling. Is there anyways to accomplish both?