I know that there is no elision with French possessive adjectives. So what's the deal with: Qui est ton artiste favorite?

You're right; in French, there is no elision with possessive adjectives: The final -a from ma, ta, and sa may never be dropped. But be careful — the abbreviations m', t', and s' are not possessive adjectives; rather, they are reflexive pronouns. Example: Je m'ennuie (I'm bored.)

To avoid awkward pronunciation with possessive adjectives, use mon, ton, or son before a feminine singular noun that begins with a vowel or vowel sound:

Right: Qui est ton artiste favorite? (Who is your favorite artist?)

Wrong: Qui est ta artiste favorite?