When children are involved then it is usual for unmarried parents to come to some sort of informal agreement with regards to how much the non-resident parent will pay towards the upkeep of the children. This is usually based on the calculation used by the Child Support Agency (CSA), soon to be replaced by the Child Maintenance Service (CMS).
As the primary carer (the resident parent) of the children you can make an application to the Child Support Agency or the Child Maintenance Service, although it is worth noting that they are unable to make an assessment if the other parent is living abroad. If one or both parents lives outside of England and Wales then the court will be able to deal with the issue of child maintenance.
As well as child maintenance, an application to the court for a transfer of property or cash lump sum for the children is possible if the parent paying the child maintenance has a large amount of assets and wealth. It is also possible to get the child maintenance raised above the minimum amount set by the CSA/CMS if this is the case.
Sometimes the court will order that the non-resident parent buys the resident parent a property to live in with the children, which will then automatically go back to the non-resident parent when the children grow up.
If you are in this situation it is extremely important to get expert legal advice as soon as possible in order to best protect your rights and the rights of your children.