Mother property

Section 15(1) of the Hindu Succession Act lays down that the property of a female Hindu dying without having left a will shall devolve firstly upon her son(s), daughter(s), and husband. So, technically, both you and your father are entitled to an equal share (considering you don't have a brother. If you have a brother who is deceased, his children may also be entitled to inherit.)

As for the fact that your mother and father were separated for over 30 years, the hope that your father loses absolute entitlement should be tentative. You can make your case to the court, but the court may or may not rule in your favour.

Both were legal heir of the deceased(your mother). if your father got divorce from your mother, then are the sole legal heir.

In the absence of a WIll both You and your father are the legal heirs of your deceased mother and both shall have equal share in the property.If your mother and father were divorced then you alone are the owner but that doesnt seem to be the case from the way you have written (saying 'separated').

Now the question is, is your father interested in his share of the property or not. If he is NOT interested he can release his rights in the property to you fully through a registerd release deed and then you shall become the only owner  Otherwise since he was separated for 30 years there is a chance you can fight it out in the court ..... but I doubt that will help. The point however would be whether your mother bought the property with her earnings and savings or was it bought in her name by your father. If your father bought it then he will have equal rights in the property and you cannot do anything about it AND  in fact he can argue in the court that since he bought the property in your mothers name he should be the sole owner. There are various possibilities depending on what you and your father want.

Did you ask your father if he is interested in the property? Since he is your father I guess he might let you take it.  Approach a well qualified lawyer with the property documents and the all other details. We can only give an idea but only a qualified lawyer who has access to your documents and details can give you the complete picture. All the best.