Limited partnerships do not issue common stock. Rather, limited partnership are composed of general and limited partners, each of whom own partnership interests in the limited partnership. A statutory trust is a different type of legal entity altogether. Since it is a trust, it is not a corporate entity, and also does not issue stock, as trusts do not have stockholders. I believe that the question of how market cap of a fund is determined should most appropriately be addressed to someone who works in finance.
Your question makes little sense. A partnership does not offer stock. A partnership can, however, be listed on a stock exchange in limited circumstances, such as MLPs and the like. Even there, however, the price on the exchange is for a partnership interest and not a share of stock. Statutory trusts are generally used for REITs and mutual funds.
The term "market cap" can be the amount of the offering or the float of the publicly traded security. The underwriter will generally determine the amount of shares to be offered at what price when going public -- that generally gives you your "market cap."
The foregoing is not legal advice nor is it in any manner whatsoever meant to create or impute an attorney/client relationship.