To find Mesprit after it runs away Note:Happens after beat Galactic at Lake Valor aslo when you beat the elite four and got the national dex go to canaclave and go to the saliors house talk to the boy and he is having a neverending nightmare from darkrai talk to the sailor and you can go to fullmoon island and talk to cressila and will run of and track it on the marking map like mesprit.
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Go to Jubilife City and go into the poketch company towards the top left of the town. Talk to the professor. Keep talking to him until he gives you the marking poketch app.
Go and talk to the owner of poketch in poketch company's building he will install the marking map app in your poketch
You can find it on any route. Just use the poketch app marking map!
You get the app from the president of the Poketch company in Jubilife City after winning the Veilstone City Gym battle. In Pearl, this app is used for tracking Mesprit and Cresselia
from a woman in eterna city's Pokemon city