Joint mortgage, TOLATA?

Hi, im hoping someone can advise me- I lived in SCotland with my ex partner for 6yrs, we were not married. We have a joint mortgage with little equity in the house.
My ex wants me to sign the house over to her but I have paid the mortgage / bills / renovations soley for the past 3 yrs, up until 8 months ago. Its the only asset I have and I feel I would rather stay on the mortgage until the kids are 18 then sell or she could buy me out at a point in the future when the property has equity? Also Can I put a charge on the house and if so what does this mean?
I fell ill in Sept 2010, I used credit cards to pay the mortgage then I lost my job and had to go onto benefits, fortunately we recieved a housing benefit which left a short fall of around £300. Which as I was in hospital my ex did a bit of bookkeeping and made up the difference.
As I am still out of work due to illness I have been sending £60 per week as maintanance for our 2 children. Even though if it was up to the CSA I would only have to pay around £10pw. One is 3yrs and the other 18months.
I have moved back to Manchester and see the children as often as I can.
She also has said she is changing the childrens sirnames as she wants them to have hers - can she do this without my consent?

bump! Can anyone help?

Are you named on the birth certificate or have you acquired Parental Responsibility and Rights?

With the exception of removing or retaining children out of the UK s2 Children Act (Scotland) 1995 states "where two or more persons have a parental right as respects a child, each of them may exercise that right without the consent of the other." That means your ex-partner can unilaterally change the children's names unless you apply to court for "prohibited steps" (and PRR if you don't have it already!) to prevent it.

You may, of course, agree most things within reason between you but in Scotland the courts tend to favour settling in the present rather than delaying. When there isn't much equity the value could easily be wiped out either by legal fees or your ex-partner exercising co-habitants' rights to financial provision. A solicitor in possession of the specific details is in the best position to advise about where you stand and what options there are.