Transfer of plot in karnataka after death of father

succession certificate is not necessary because it is necessary for collecting money only belonged to the deceased. As and when your mother died the plots automatically vest with her legal heirs i.e. son daughter. please inform whether any sale deed was executed. if any sale deed was executed by developer in your mother's name you have to change the revenue records by mutations proceedings.

First obtain a legal heir certificate and then draft a settlement deed within the family (Drafted by Advocate)  giving all rights to your mother and register the same.  Get mutation done as per laid down procedure either with Revenue authorities or Corporation / Municipality.  Submit Legal heir certificate, copy of settlement deed in your mother and mutation certificate and demand developer for doing needful.  He is bound to accept this.  If not, make a simple complaint in District Consumer Forum for deficiency of services for not changing the records even after attending to legal formalities.  All this process is simple and may not involve huge costs.

confirm status of the plots first are they registered in your father's name or is it just a booking that was done

If it is immovable property succession certificate is not necessary .so all of u issue legal notice to him if he denies file suit against them in court it doesnt take much time. To decide.

Has the conveyance as to purchase of the plots completed and deeds duly executed? Who is in possession/occupation of the property?