The options as I see it are:
a. We both aim to pay 50% deposit and payments, meaning I would take on a larger mortgage than I need, but it's less hassle probably.
or...
b. I pay say 70% deposit, partner pays 30% - we both share mortgage payments equally but I retain a bigger share of house ownership (if we ever resell).
or...
c. Or paying while paying 70/30, my partner could gradually pay me back via some sort of legal joint mortgage agreement so that we both own the house equally.
or...
d. theoretically, if we bought something really cheap, I pay 50% total home price. Partner pays whatever is affordable and takes a single mortgage to pay the remainder due. So again retaining 50% ownership each.
And since you mention it, if one person ups and abandons the mortgage, are they still entitled to be named on the deed as a co-owner?