So... is Princess Princess finished or not?
NO, it is not finished.
Why?
The anime finished before the manga:
Anime finished: June 22, 2006
Manga finished: January 01, 2007
MangaUpdates contains information about the anime adaptation and indicates that it is incomplete.
Watching Order (by release date)
Here you have all the anime relations we detected ordered by release date, so you can see the reason for this status in context and also use it as watching order.
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Synopsis
Princess Princess centers around Tooru Kouno, who transfers to an all-boys school and quickly discovers he's considered very attractive.
Much to his dismay, he learns about a bizarre school tradition: selecting attractive first-year students to crossdress as "Princesses" to uplift the student body's spirits.
Tooru finds himself nominated for the role, joining two other boys, Yuujirou and Mikoto, who already fulfill this duty.
The anime explores how Tooru grapples with this unexpected situation and his feelings about participating in this unusual school tradition.