IIn NSW, under s 57(1)(d) of the Succession Act, your Former Spouse (or De Facto Partner) may be Eligible to Contest your Will. However, your Ex will only be deemed an Eligible Person where there are Factors Warranting the making of the application. The case of Lodin v Lodin provides a useful discussion as to what will constitute factors which warrant the making of an application.
It is common for testators to transfer property or assets to their intended beneficiaries prior to their death, in an effort to avoid any potential challenges to their will. The logic being that an applicant will be unable to challenge the will where the estate has no real value. However, in NSW transferring your assets before your death will not necessarily prevent a family provision claim from being made against your estate and in particular circumstances the court may make a Notional Estate Order.
Family Provision was traditionally seen as a means of giving effect to a testator's moral obligations or duties to provide for their dependants and family members. While, this approach has been questioned, the relevance of moral obligations or duties to family provision claims was confirmed in Vigolo v Bostin.