Re: Not on loan but on title?
There is no legal reason why both co-owners have to sign the note and deed of trust and thus be "on the loan." As a practical matter, most professional or institutional lenders don't like this situation, and it may be very hard to find a loan on acceptable terms.
The reason is that if only one co-owner pledges his or her interest as collateral, the lender not only has 50% less collateral, it also has a basically unmarketable asset -- half-interests in houses are not hot items in the foreclosure market. Remember that with purchase-money loans, the lender must look to the collateral alone, and has no recourse (usually) against the borrower(s) personally. And, of course, a 50% owner cannot pledge more than his/her 50%.
There is another scenario -- where one member of a couple already owns the house 100% and is the only borrower. The owner-borrower then sells or gives as a gift a 50% interest to his/her partner. Deals like this are plagued with problems. First, the sale or gift of a half interest may trigger a "due-on-sale" clause in the note and/or deed of trust. Also, such deals are usually put together in the heat of passion, not well thought out, undocumented, and usually grossly unfair to one partner or the other.
Finally, I should mention that the new domestic partners law in California makes home ownership more like it is for married couples when domestic partners register and agree to co-own property. This law and its effects is outside the scope of the rest of the answer given.
If you contact me with more particulars, such as the current and proposed status of ownership and loan liability, and your reasons for doing these transactions, I'll try to give you a more personalized answer, gratis.