How can I prove the immigrant officers that I have significant ties in my home country?
Are there any documents that I need?
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Based on your tags my answer will be relevant to a non-immigrant visa for the USA.
You need to prove that you will not stay in the US indefinitely, and that you will return to your home country, hence the demonstration of the 'significant ties'. These may depend on your age too. As a rule of thumb this can include, but is not limited to, the following in your home country:
To summarize, anything that will convince the officer that you will surely return to your home country can be used as proof; and yes that includes your appearance, confidence while you're sitting in front of him/her presenting your case. It all boils down to how well you can present your case and convince the officer that you will return once the visa expires.
Coming to the second part of you questions, documents that you need: any related documentation of the above mentioned points. I will list down examples in the same order below:
Hope this helps.
Having a job in your home country, especially a full-time one. Owning property there, or having a lease for property (e.g. a rented apartment or home where you live). Having reasonable to significant amounts of money in banks in your home country. Having family members back home.
As for documents, it's not usually necessary to have proof of these things, since some of them can be proved using electronic devices (e.g. bank balances) but if you feel there's a significant chance of being refused admission into a country (you haven't given us any details of where you're from nor where you're going), take some bank statements with you, a notarized copy of the title deed from your home, your apartment/home lease, and such with you.
Immigration personnel want to be convinced that you can afford to visit their country using assets you already have, and won't try to immigrate there without proper permission. Having attachments to another country will convince the officer that you're a genuine tourist.