How wide should the range hood be

The range hood should as a minimum cover the width of the range. The reason for this is that the hot vapours from the range expand as they billow up. Under ideal circumstances the range hood should be wider than the range by 3" either side - however this is not always possible.

Wall Range Hoods:
Wall range hoods should as a minimum be the same width as the range top

Island Range Hoods:
Island range hoods should as a minimum be 6" wider than the range top. The reason is quite logical - island range hoods are exposed to cross drafts in the kitchen from ventilation systems and even people moving around.

Here is a picture of a 12' wide range hood - the range top is a 30" induction cook top and we provided a 600cfm internal vent blower with stainless steel mesh filters directly over the induction cook top - 30" wide. The remainder of the island range hood underside was custom fabricated stainless steel panels with lighting. The lighting is controlled by two dimmable range hood light controls - one controlled the kitchen hood lighting above the induction cooktop and the other rangehood light controlled the island rangehood lights on the perimeter:

Link to range hood design information