Abstract
We study the radio properties of the optically luminous subclass of quasars at $M_{V} \approx -26.0$ ($H_{\rm 0}=100$ km s -1 /Mpc, $q_{\rm 0} = \frac{1}{2}$; Teerikorpi [CITE], [CITE]; Papers I, II), after first results on double sources in Paper I and the confirmation in Paper II that optical activity abruptly increases when one crosses the gap around M V = -25.5 between AI and the optically fainter quasars. AI double sources define the upper envelope in the size vs. redshift diagram, so AI quasars are not only optically the most luminous, but also in radio the largest objects in their redshift range (from 0.5 up to at least 1.6). They are typically good FRII objects, mostly with a small lobe-distance asymmetry Q . A part of the scatter in size is due to orientation, which reveals itself via the size vs. core strength dependence, such as is expected from relativistic core boosting with $\Gamma \approx 5{-}8$. This relation appears for symmetric sources ($Q Q increases from AI to the edge of the fainter population, which, down to $M_V \approx -24.8$, contains unusual double sources, with a more versatile and less symmetric lobe structure, often with a hotspot in the trailing edge.
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