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Can I drive a single QHD monitor off my late 2012 mac mini or could I
daisy up another 1080p or QHD(preferably) to it?
No to QHD (3840 x 2160), no matter where you connect it.
The Late 2012 Mac Mini can drive two external displays:
The HDMI port can go up to 1920 x 1200.
The Thunderbolt port can go up to 2560 x 1600, using a Thunderbolt
display or Mini Displayport adapter/cable to other interface types.
Most Mini DisplayPort adapters will be limited to 1920 x 1200 (e.g. VGA,
HDMI, single-link DVI). With Mini DisplayPort to DisplayPort or a
dual-link DVI adapter it should be possible to get 2560 x 1600 via
You can daisy chain two monitors from the Thunderbolt port, but the
first one has to be a Thunderbolt display. The Mini's HDMI port can't be
used at the same time as two monitors on Thunderbolt.