  This paper studies gradient almost Ricci-harmonic soliton with respect to a
fixed metric. We rely on analytic techniques to estabilish some basic elliptic
and integral equations for the structure of almost Ricci-harmonic soliton which
generalizes that of Ricci-hamonic solitons on one hand and that of almost Ricci
soliton on the other hand. The consequences of these formulas in relation to
classification and rigidity results for gradient almost Ricci-harmonic solitons
are also discussed.
