Do I receive anything concrete to say that the home is mine, like a deed?

Yes you do. Within a couple of weeks after the closing of your purchase you should receive a complete reporting letter from your lawyer confirming all relevant aspects of your transaction. Included with the reporting letter you should find the receipted printout confirming the registration of the transfer and the mortgage showing that you now own the property subject to the registered mortgage, copies of all documents you signed at your lawyers office, copies of all documents your lawyer received from the vendor at the closing and your lawyer's account and trust ledger statement showing where the purchase money came from and how it was spent. There may even be a small refund cheque for you if certain costs were over-estimated. It is worthwhile reviewing this material on receipt and it definitely should be stored in a safe place such as a safety deposit box or fireproof safe.