> I need to inform immigration before I leave and/or after I come back?
You do not need to let immigration know when you leave, however you must let immigration know when you return. When you return, you will file a TM30 no later then 24 business hours after you return. You can do it in person, or use one of the following three programs:
Apple:
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Android
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Online:
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> and assume that they have to register me anyway
Yes, the hotels will file the TM30 for you.
>Do I still have to do something myself?
Only file the TM30 when you return.