I will be purchasing a new car fairly soon here, and could help my SO out a lot by having her "take over" payments on my current car. I've heard this term colloquially, but I'm not sure how it works in practice. Is it a matter of approaching the lienholder (a bank) and having the leasee information changed? Or is this just a short way of saying something different?
The phrase doesn't mean anything specifically.
Your SO could start paying the payments, but the title and lien would remain in your name. If you wanted to change the title or lien to be in her name, you would have to sell the car to her (sales tax would be involved but the process would be relatively painless). You could sell her the car for a pretty cheap price, but not $1. (unless the depreciated value of the car was less than the rest of the loan amount).
You could draft up an agreement that if you break up or something, she agrees to buy the car from you for $x dollars minus all the payments she has made on the car.
I think this phrase originates from when it was common to have an assumable mortgage. In that case, you would "take over payments" and the loan would become yours.
Assumable Mortgage: A type of financing arrangement in which the outstanding mortgage and its terms can be transferred from the current owner to a buyer. By assuming the previous owner's remaining debt, the buyer can avoid having to obtain his or her own mortgage.