do shared albums owned by others take up storage space on my phone?

Greetings, colemanjs.

Welcome to the Apple Support Communities. Managing your device storage is vital, so we can understand why you’d want more information. 

We see that you reached out to us from: How to share albums in Photos on your iPhone, iPad, and Mac 

Have you saved the photos and videos from the shared album? If so, they would be saved to your library.

We hope this helps! Thanks for being a part of the community.

Sincerely.