A word or phrase for deliberately trying to lose something

Is there a word or phrase to express when someone wants to lose his nasty cat, deliberately trying to leave it in some jungle or street? He tries to lose it in the streets so that it won't come back.

For example: Estelle is trying to _________ her cat.

Abandon

verb (used with object)
1. to leave completely and finally; forsake utterly; desert:
"to abandon one's farm; to abandon a child; to abandon a sinking ship."

Hence:

Estelle is trying to abandon her cat.

Lose works just fine.

Lose — ODO

(US, informal) verb 2.3 Get rid of (an undesirable person or thing)

"lose that creep!"
"They need to lose that awful voiceover."
"You need to lose that creep before he pressures you into more things you don't want to do."

Synonyms: ditch, abandon, dump...

I think abandon works here.

Cease to support or look after (someone); desert:
her natural mother had abandoned her at an early age

Reference:
http://www.oxforddictionaries.com/definition/english/abandon