court (esp. AmE)
bankruptcy, divorce, habeas corpus (AmE)
She filed a habeas corpus petition on Padilla's behalf.

file, submit
hear
The petition will be heard tomorrow.

accept, approve, grant
Her petition for divorce was granted.

deny, dismiss, oppose, reject
The district court has opposed the petition by the local electricity company.

petition for
He can file a petition for writ of habeas corpus.

petition on behalf of
a divorce petition on behalf of Terri Jones

protest (esp. BrE)
10 000 people signed a protest petition.

online
nominating, recall (both AmE,politics)
The deadline for filing nominating petitions for the primary election was Tuesday.
Two million people signed the recall petition.

sign
draft, launch, organize, raise (esp. BrE), start, write
We've started an online petition.

draw up, get up (esp. BrE), set up (esp. BrE)
The players drew up a petition and presented it to the coach.
They've threatened to get up a petition against the plan.

circulate
The company had actively circulated petitions to get rid of the union.

support
deliver, present, send, submit
They delivered petitions with nearly 20 000 signatures to the Senate.

ask sth, ask for sth, call for sth, demand sth, request sth, seek sth, urge sth
a petition asking him to reconsider

oppose sth
The petition opposes the closures.

support sth
The petition supports the plan to rebuild the road.

petition against
We're organizing a petition against the proposed building plans.

petition by, petition from
a petition by local residents

petition for
Local government supports the petition for a new hospital.

petition in favour/favor of
a petition in favour/favor of reform