There is a new quest for star, just found it today looking for large monster groups.
Quest name: The mark of going home
Location: Go to South Island, enter Maka Cave, follow the path to the Highlands:
On the Highlands map you'll find a breadcrumb path. Pick a bread, talk to the girl and follow the path to find and fight the bird:
Reward:
500 exp
1 star
3 Ship Voucher.
Having a signature is like keeping a gremlin.
Just don't overfeed it, don't make it wishy-washy and you'll be a good responsible Signature Keeper :]