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A criterion for quadratic or higher growth of group automorphisms isestablished which are represented by graph-of-groups automorphisms with certainwell specified properties.  As a consequence, it is derived (using results of a previous paper of theauthor) that every partial Dehn twist automorphism of $\FN$ relative to localDehn twist automorphisms is either an honest Dehn twist automorphism, or elsehas quadratic growth.

Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy