It is not only size. It is also liquidity.
In general terms, the top 300 will be followed by some institutions and some brokers. The top 50 to 100 companies will be followed by nearly all of them.
However, if there are a few large shareholders and not many shares available to trade, institutions will find it not worth their while. Brokers will find it even less so - because if they cannot generate business, why do the research.