
This would be called a loan of bitch agreement and for the purposes of whelping and breeding the litter the person woudl own the bitch and be listed as the breeder. What arraangements you come to between you about who gets what etc is up to you to draw up and sign.
I ahve bred a litter like this for someone who could not through ill health whelp their bitch. There were no problems with the arrangements. Originally they were going to ahve a pup, but after the mating they found they couldn't so I paid them the price of a puppy/stud fee for the use of the bitch.
Saying that I would never do it again. The bitch was unwell when she came to me with terrible dirhoea which by whelping left her ill prepared and we ened up with a C sectiopn and an underweight bitch. She could have died and things could have gone terribley wrong, and this could with the best will in the world have caused problems for me, as there woudl have always bveen a niggling doubt in the owners mind about my care for their bitch.
If you do this get everythign in wrtinting not just the loan of bitch agreement.