It may not be as simple as that. First, it sounds like your father has a mortgage on the property. A transfer could trigger an event of default on the loan and allow the bank to demand the loan.
Second, depending on the age of your father and his health, a transfer of this sort could result in a disqualification for public benefits should your father require them within the next five years.
It sounds like your father should speak with an Elder Law Attorney to do some estate planning.
Read the BOA document. I'm sure it as a paragraph that gives the lender a right to accelerate the debt upon any change in ownership. Your quit claim deed may just trigger a default under the DOT.
Also, without a title company doing a complate lien search, you don't know what items other than the bank loan will attach to the property before your interest.
And what makes you think you will assume the loan? Upon Dad's death, the bank will want you to refinance them out of the deal.
As the other attorneys have stated, it's usually not a smart idea to do what you're proposing. In addition to what they've said, your father would be making a gift to you and would be required to file a gift tax return with the IRS. In addition, when you sell the home, your "cost basis" would be the price he paid for the home (plus any "capital improvements").... if you inherit the home, your "cost basis" would be the house's value on your father's date of death (under current tax law, at least).
Your father would be far better off legally to spend some money on getting a revocable living trust. If he believes he's going to need to qualify for Medi-Cal, then he should have the trust prepared by someone who is familiar with all of the Medi-Cal rules (they are complex!!).
The information you obtain at this site is not, nor is it intended to be, legal advice. You should consult an attorney for individual advice regarding your own situation.