As much information as you wish. You can run a prequalification request through the complete underwriting process and still not have an application for HMDA reporting purposes, providing you don't have a qualified pre-approval program; and as long as you do not have an identified property you don't have an application for RESPA purposes. Or you can simply tell the person no because you don't like the way they look and then you have an application for Reg B purposes under 202.9.
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The opinions expressed are mine and they are not to be taken as legal advice.