You do not need a router for a wireless printer. I just bought the new HP C8180 wireless. Highly recommend wireless. I have mine out of sight in the closet.
I would think you still need the wireless router in order for the two machines (printer & computer) to "talk" to each other. They each have a builtin wireless radio, but you still need the router to form the network.
kev
keeping my ears open for oddball cards of Rose from the 60's and 70's.
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keeping my ears open for oddball cards of Rose from the 60's and 70's.