Boilers are said to be most efficient when operating at 70-80% of their rated maximum output. Why is the boiler most efficient in this range and not across the entire operating range?

Thank you

The efficiency of a boiler is a combination of the efficiency of combustion and the efficiency of heat transfer. Both of these are largely affected by the turbulence of the gas flow through through the boiler.  The turbulence depends on the flow path and the flow rate, and these are determined by the size and geometry of the boiler fire-side.  As the boiler fire-side dimensions are fixed for all operating conditions, the turbulence of the gas will change across the operating range, affecting the efficiencies of combustion and heat transfer along the way. 

Through a combined process of design and experience, boiler manufacturers have generally achieved an overall maximum efficiency when operating at 70-80% of maximum rating.

Bear in mind that the boiler will typically produce steam to match a fluctuating demand, and that continued running at maximum efficiency is pretty much impossible.  The best your can do is to maximise the combustion efficiency by adjusting the air/fuel ratio, and to keep the heat transfer surfaces clean.