If the funds are used for a house purchase, there may other issues than just the transfer. The title will be in your name (or at least someones if it isn't for you) creating a connection. It may never be an issue but if you, or the title owner are ever audited or questioned where the funds come from etc, that anonymous transfer won't help you. Also, as you say its a deposit, the bank offering the mortgage might need you to document the source of funds for the deposit.