Multi computers connecting with one External Hard drive

No, connecting a hard disk to multiple Macs through a hub isn't going to work. The usual way to share content is through a network.

Assuming your several Macs are already clients on the same network sharing that hard disk's contents is not difficult. Read Set up file sharing on Mac - Apple Support. The logical choice would be to connect it to one of your Minis assuming it remains present on the network and does not need to be moved very often. Let it sleep in the usual manner. It will wake if needed.

If your network is created by an AirPort Time Capsule or AirPort Extreme Base Station it's even easier: Share a USB hard disk on your network in AirPort Utility on Mac - Apple Support. Unfortunately Apple discontinued them a while ago.

David Pottinger Said:

"Multi computers connecting with one External Hard drive: I have 3 MACs: MacBook Pro, and Two Mac Mins I'd like to use one External Hard drive. With all three connect directly to the hard drive (maybe through a Hub?) If I have to I guess I could do it through the WIFI network I use but not looking forward to that."

-------

Use NAS (Network Attached Storage):

Have a Router? Connect your external hard drive to your router. From there, you would be able to access it. But, you need to have this associated to your network. This would be considered NAS.

You can move a directly-attached external drive between computers … but you shouldn't directly attach a drive to multiple computers at the same time. (Even if it, say, has USB 3 + eSATA + FireWire ports.)

Each computer will think that it "owns" the entire drive, and they will completely corrupt each others' data. If you want multiple computers to use the drive at the same time, you either need to use a standalone NAS, or have one computer own the drive and serve it up to the others (act as a NAS for the others).

"Multi computers connecting with one External Hard drive: [...]Can you connect a router to a Wi-Fi system and then connect your own computers to your router (I guess it's Wi-Fi. )I am stuck with having to use the facilitys Wi-Fi since I live in a Senior Living facility sometimes it is WY-IF instead of Wi-Fi. If I use a router as the NAS even if the facilitys Wi-Fi igoes down I can still communicate between MACs right?[...]"

-------

Connecting a Hard Drive to a Router:

If there is a USB hub on your router, then connect your hard drive to the router. From there, officially, would be called cloud storage.

Accessing this Storage:

As ling as everyone on the network has access to it, then they will see it --from Macs to PCs to PDAs to Phones to Gaming Consoles and more.

Technically yes, after all that's how the Internet functions, but not all networks permit the addition of an additional router on their system. In fact I'd be surprised if they did.