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I assume I'd look around, get recommendations, then go to one and get a pre-approval which entails a hard pull. Once that's done, do you simple go to different lenders and ask for their estimates for a similar loan or do they also need to do their own pulls, collect income/tax/debt details from you as well?
Or does the lender shopping start after one has an accepted offer on a house?
each lender will have to do their own hard pulls and complete and totally separate application when you decide you want to apply with them. however, if you get a pre-approval from one place, you can take your scores and gfe and 'shop'. meaning, you can you take that information and discuss what products other lenders have that may fit your current credit profile (credit scores, downpayment, etc). you can also ask them to give you an idea of what the closing costs would be for the price of your house. closing costs will vary, but the prepaids (amounts that will go directly to escrow account) will not vary.
if you like what the other lender is offering, you can decide to complete the application process with them and they will pull your credit at that time.
Getting rate quotes before securing a property is not productive or useful. Other than rate, you want to ask about fees, underwriter inhouse or not, do they have direct access to the underwriters, what is their communications process, how often can you expect to hear from them. ....
The questions are driven by what's important to you. Let your instincts guide you.