Who inherits when there is no will
If a Hindu, Sikh, Jain or Buddhist dies without a will, the Hindu Succession Act 1956 sets out a fixed order of heirs, beginning with certain close relatives who inherit together in defined shares, before moving to a wider circle if none of them survive. The Indian Succession Act 1925 applies a different scheme for other communities, and also governs succession under a will generally. Establishing exactly who the legal heirs are, and in what shares, is usually the first practical step, since banks, registrars and other institutions will ask for this before releasing any asset.
Probate, letters of administration and succession certificates
Where a will exists, probate is the court's formal recognition that the will is genuine and can be acted upon; it is compulsory for wills made within the ordinary original civil jurisdiction of the High Courts of Calcutta, Bombay and Chennai, and for wills affecting immovable property situated within those areas, and is often obtained elsewhere too as a practical matter of proof. Where there is no will, letters of administration serve a broadly similar function, authorising a named person to administer the estate. A succession certificate is narrower still, and is generally used to collect debts, securities and similar movable assets rather than to deal with immovable property.
Why a nomination is not the same as inheritance
This is the single most common misunderstanding families run into. A nominee named on a bank account, insurance policy or company shareholding is, in most circumstances, only authorised to receive and hold the asset on behalf of whoever is legally entitled to it under succession law; the nomination itself does not determine ownership. A person who is not an heir can end up as a nominee, and can find themselves required to account to the actual heirs for what they received. Anyone relying on being named a nominee as if it settled the question of inheritance is very likely mistaken, and this misunderstanding is behind a large share of the family disputes we see.
Assets spread across more than one country
Where a family holds assets in India and abroad, it is generally more reliable to have a separate will for the Indian assets, drafted to work with, rather than contradict, any will made under a foreign jurisdiction. Coordinating the two, so that neither accidentally revokes the other and the overall intention is clear, is worth doing while the person concerned is alive and able to give instructions, rather than leaving heirs in different countries to reconcile two documents after the fact.