How does shareholding pattern, marketcap change after listing subsidiary?

A publicly listed company say, A has a market cap of say, $30 billion. It has an unlisted subsidiary (100% stake) B whose marketcap as perceived by the market is $15 billion.
1) So is it fair to say that 50% of the shareprice of A comes from the value of B.?
Suppose the company B is a high growth company and A decides to list B separately. Suppose it wants to retain 50% stake. Remaining 50% is offered to the public.
2) Will it have to distribute the 50% stake that it owns as per the existing shareholding pattern of A? Isint that necessary considering that the reserves and surpluses of A over the years has been diverted as investment for B?

Market capitalization is the total value of a company's shares trading in the stock market. Therefore B does not have a market capitalization because its shares do not trade. It is possible, however, that the market perceives that 50 percent of A's share price derives from its ownership of B.

How does A list B's share? It can make an offer to sell 50 percent of its ownership of B in the market by listing those shares on an exchange. Those shares will fetch whatever price the market assigns to the shares, and A will receive the cash from the sale. The market price determined in the market for B now also determines the value of A's share of B, which may be more or less than the value previously assigned to B indirectly through the market capitalization of A.

It is not clear what you mean by "as per existing shareholder pattern of A." Nor is it necessarily the case that A's surpluses were diverted to B. The value of B may have been earned by B through its operations. In any case, the market will determine the market capitalization of A and B after the divestiture.