From the stand point of being properly diversified it would be difficult using 3 independent brokers unless they were talking to each other (highly unlikely), so I would vote for a single common broker. Also, pay attention if you decide to go with a single broker, as there may be opportunities to limit taxes or change investments to save future taxes.
Hope this helps, good luck with your project.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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