Kitchen Large Electric Appliances - Dishwasher over flow thing

I'm in the early stages of replacing my counter tops with granite. My current sink has a dishwasher over flow thing mounted on it,but in looking at magazines to get some ideas I see a lot of photos of finished projects that don't show this over flow thing on their sink like I have. My first thought is that they don't have a dishwasher but a lot of the photos show a dishwasher. Is there some kind of new way to provide a over flow but under the cabinet hooked to the under sink plumbing? Sure would be nice to have one less item on top.

Its actually a vent (or vacumn breaker?), I'm not sure why they are required in some installations and not in others.

Some of the experts will be able to tell you, give 'em a while.

These vacumm break vents are needed to prevent the drain fluid backing up in the drain due to partially clogged or poor drain systems without adequit venting up to the roof.

Some jurisdictions require a countertop type anti-siphon device:

http://paragoninspects.com/images/appliance/dishwasher/dwairgapcountertop2500.jpg
Fig 1. Example of typical countertop anti-siphon device.

some will allow the installation of a "high loop" instead:

http://paragoninspects.com/images/appliance/dishwasher/dwhighloop1500.jpg
Fig 2. Example of typical under sink "high loop" installation.

Some dishwashers (according to the manufacturers installation instructions, anyway) don't require external anti-siphon protection, their instructions may or may not be accepted by the local authority having jurisdiction (AHJ).

So what it really comes down to is what's acceptable to your local building department.