That is a healthy concern to have. There's no problem asking the landlord what happens to this application after you're done filling it out. Ask him what happened to the application if you get the apartment, and if you do not.Keep in mind if you get the apartment, the applications going to crucial information for the landlord to contact you your next of kin or to find you if you run out without paying rent.Also, due to housing laws, discriminatory housing lawsuits can be filed by prospective tenants if they do not receive the apartment. So it would be appropriate for the landlord to hold onto your application even if you did not get the apartment for a bit of time, but make sure that they have some plan for that.