Fractional shares are not a standard. You can not register as a shareholder at a company using fractional shares and you can not trade on the stock exchange with fractional shares. So brokers can not trade fractional shares between them. Fractional shares are something that is implemented internally at a broker. They basically find two or more clients who wants to buy fractional shares and then the broker buy the full share and splits the ownership between the clients. It is theoretically possible for two different brokers to allow trades of fractional shares between them but it would be a bit messy as those trades could not be fulfilled and had to be reversed at some point or made into full shares with other trades. So for now we need stock splits.
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