Cost of acquisition of shares

Let me know

if the Mr. A expires, and Mr. B, being the nominee, receives the shares of that demat account.

- cost would be as hold by previous owner, no capital gain wil arise for B unless he sells shares, and cost of holding will be same as previous owner.

If the Mr. A, on his own accord and free will wants to transfer shares to his nominee Mr. B while Mr. A is still alive.

- if B is relative to A then above reply is correct, otherwise the cost of shares would be subject to gift tax at prevailing  market value on the date of transfer.