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If there is a warrant out for your arrest, the police can arrest you wherever they find you.
They have the last address you filed with the state, but they don't have to arrest you at your home. That warrant would give them the right to search that address looking for you. But it doesn't mean that if they find you elsewhere they have to wait for you to visit your neighbor's place to take you in.
An arrest warrant is specific to the person and not the place. A search warrant is place-specific.
Yes, they could be staking out your former residence to try to get you coming or going. If you are concerned about this, it's a good time to seek out local counsel to protect your rights if the police find you and pick you up. But most importantly, if they find you, you should exercise your rights under Miranda and decline to submit to police interrogation.
Do NOT let the police question you about any incident. Tell them that until you have a lawyer you do not wish to answer questions. That's your right and they cannot hold that against you. But the minute you start answering questions about suspected criminal activity, anything you say to the police can be used against you if you're arrested and brought to court.
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