Cause

saajan_12

This forum likes to get tied up in the meaning of fair. As in of you agree that you pay nothing but get an equal share in the house because of other work you do, that's fair because it's what you agreed. However assuming you are looking for the most equitable way, only considering financial contributions, there's a few ways you can do it:

1) you borrow the extra 20k deposit from partner, and both own 50 /50 from the outset. You then pay partner back the 20k separate to mortgage contributions, possibly with a pre agreed interest rate. 

Pro: keeps the house deeds simple

Con: little protection for partner if you don't pay

2) you take on more of the mortgage and own 50/50.
So your 30k deposit is 4.5% of the property value, so you borrow the remaining 45.5% of the property value to total 50%. So 45.5%/85% = 53.5% of the mortgage payments including interest. Partner pays 46.5% of the monthly mortgage.
If you sell / break up before the mortgage is paid off, then you each get half the sale price but you pay off more of the mortgage (53.5%) from your share. 
Pro: you get the extra equity at today's price since that's when you made the commitment but you do pay something for not having the money upfront, in the form of paying slightly more of the interest.
Con: if you end up in negative equity, you have to top up with your own funds to pay back the partner.

3) if / when you have the money, buy more of the property at the market value at the time.
Pro: this makes more sense if you're not sure whether you'll be and to buy more and are not committing to buy more yet.
Con: hassle of getting another valuation. You both have to accept you may not buy the higher share.

Overall 1 and 2 are similar, both apply if you'd definitely want to equalise the shares. You're effectively borrowing the extra money, so lose out on interest. If you're not sure, then you stay with the unequal shares now, and if you can buy more in the future, you do at the price then, but you lose out on the value increase (or decrease). Personally I'd pick (2)