i have recently gone through this. We had the house valued by 3 separate estate agents. We then subtracted the remaining mortgage from the valuation. The answer was divided by 2. This equated to the amount each person would get if the house was sold. So i bought my partner out for this amount.
Re stamp duty: If you are buying out partner for less than 127,000 (ie, if partner's share is less than this) then you do NOT pay any stampduty. There is thread somewhere on the site about this. In any case, the revenue commissioners will confirm.
You will maintain your FTB tax relief allowance for the remainder of your original 7 year term.
Regarding the banks, i just told the mortgage company the truth. Your mortgage will be 'transferred' into your sole name. For this to happen, you need a solicitor. The process is exactly the same as buying your own house, but as the bank already have your details, that side of it is quickly dealt with.
We both used the same solicitor's firm and our costs were very low.
hope this helps!