Any debts in your sole name are your responsibility and the same applies to your ex-partner, debts she brought to the relationship are not your responsibility if you are not named, any debts where you or your ex-partner are named jointly and severally are the responsibility of the persons named for the full amount not just their proportion and the creditor will often pursue the person they believe offers them the best chance of success. You or your ex-partner will probably also be responsible for any debt where you or your ex-partner have been guarantors if payments are not maintained.
If your mortgage is in your joint names you are both responsible for payment the mortgage provided will not care who pays, but the full amount should be paid not just your proportion. If it is not you will fall into arrears and the mortgage provider will ultimately seek possession of the property. If any of your creditors have had judgement entered against you or your ex-partner they can apply for a charging order which, if granted and they usually are, has the effect of changing an unsecured debt into a secured debt against the property.
As several people have suggested take advice as soon as possible particularly as there are children involved.