Irrespective of whether you have a will or you die intestate, your executors or administrators will usually contact the company to inform the company of your death and will request either that (i) the shares are re-registered in their names as the "transmittees" to hold during the administration of your estate; or (ii) that the shares are transferred directly to your heirs. Until the shares are registered in the name of someone other than you, some of the rights attaching to them (eg voting rights) may be suspended.
Transferring or re-registering your shares will be subject to the provisions of the articles of association of the company (and also the shareholders' agreement if there is one). It may be that your shares must first be offered for sale to the other shareholders at a specified price before they can be transferred to your heirs; or it may be that your death itself is a "compulsory transfer event", which means that your executors or administrators must offer the shares to the other shareholders (in which case it will be the sale proceeds that will then form part of your estate).
It is therefore vital that you understand how the constitution of the company affects your estate's rights to your shares on your death and this should be reviewed before you draft your will.
The content of this article is intended to provide a general guide to the subject matter. Specialist advice should be sought about your specific circumstances.