Since he is a joint owner - he would be considered to own 50% of the house unless you both did not own in equally.
He will also be considered liable for 50% of the mortgage.
Since the fair market value is greater than the purchase price, if father quit claims the house to the daughter than he would be considered as gifting 50% of the fair market value to her. This will be reduced by 50% of the mortgage that daughter takes over.
Normally a person can give up to the annual exclusion amount $12000 for 2008 to a person, every year ($ 24000 in 2008 if spouses joins in for the gift) without facing any gift taxes and note that such amounts do not count as part of your $1,000,000 lifetime total.
Further, IRS allows a person to give up to $1,000,000 in gifts, total, in their lifetime, before they start owing the gift tax. (This gift is not per (donee)person but its a per donor limit). So you can make gifts that are worth up to a million bucks during your lifetime without paying the gift tax. . Even if you do not owe a gift tax because you have not reached the $1,000,000 limit, you are still required to file gift tax return if you made a gift that does not qualify as excludable.
Hence, if your father has not used up his life time exclusion, she can gift the house to you without owing any gift tax. He will however, have to file a gift tax return and report the gift to the IRS.
You, as a recipient of the gift, will not owe any tax on the gift received.
Let me know if you have any question.
Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.