Your query is slightly confusing. Do you have a Legal Hier certificate? Now regarding obtaining a Legal Hier certificate / Succession certificate please follow other experts who have already replied.
Coming to the Physical share certificates, there is now a long road ahead as you now will have to approach all the companies (Registrar & Transfer Agents) and will have to fullfill a Share Transmission process. It requires Legal Heir Certificate/Succession Certificate/Will. In the absence of the same the process is quite cumbersome as then you will have to produce Indemnity, Sureity , Letter of Disclaimer (in case if you have more number of siblings), Signature attestation from your Bank etc etc. Also note that common Share Transmission process and supporting documents will NOT work. you will have to submit different set of documents for each of the company. Hence, first analyse the shares what you have, see the net worth of the shares and only those shares who are offering returns, please follow the Share Transmission process. On an average it takes 30-45 days. Better to talk with your DP or an Financial Expert who can guide you in this matter.