DVR for Dummies (aka - me)

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We currently have a 16 channel multiplexer with a time lapse VCR.  It's
about 8 years old and needs replaced.

We have been looking into DVR systems and DVR cards available on Ebay
and elsewhere.  (I won't get into why we'll never purchase CCT
equipment from ADT ever again).

We currently run 12 cameras, although we have the capability for 16.

One frustration with our current time lapse VCR system is that our 12
cameras cannot be recorded simultaneously, instead it records camera 1
for a few seconds, then camera 2 for a few seconds until it cycles
through to camera 12 and then back to camera 1.

Can DVR systems record all cameras at once, or do most still cycle
through each camera, one by one?

If DVRs can record simultaneously, is this a feature that is typical,
or is it only available on high end equipment.

Thanks in advance for enlightening me!