Yann Sicamois, the webmaster of the site Liv Tyler Web Site, did a great job for Liv's birthday last year. He bought her a star.
He called it "Liv Stellar Project" and bought a star called Liv Tyler in the Ursa Major Constellation.
Here's where the star is located:
And here's the official certficate:
If you want to know more about this project you can look at his Liv Stellar Project page or at his site Liv Tyler Web Site