Links/Slugs ?

Okay when I go to a parent category page, I get a url of:
Example: myblog.com/parentCategorySlug/
when I go to a child category page, I get:
Example: myblog.com/parentCategorySlug/childCategorySlug

Which is normal.
What I cant figure out is what PHP Code can ECHO these links when Im on the pages, for example if Im on a child category page, I want to ECHO only: /parentCategorySlug/childCategorySlug WITH NO “myblog.com”
and when im in a parent it echos: “/parentCategorySlug/” WITH NO “myblog.com”

This PHP will be put in category.php which means it should work with all parent and child category pages wordpress generates.

Also if its possible to put it on tag.php and archive.php etc?

I been trying all the wordpress functions and codes from Documentation but none get me this link.

Please guys I need help since Im launching this site tomorrow night!
Thank you!