Let
μ
\mu
and
ν
\nu
be probability measures in the complex plane, and let
p
p
and
q
q
be independent random polynomials of degree
n
n
, whose roots are chosen independently from
μ
\mu
and
ν
\nu
, respectively. Under assumptions on the measures
μ
\mu
and
ν
\nu
, the limiting distribution for the zeros of the sum
p
+
q
p+q
was computed by Reddy and the third author [J. Math. Anal. Appl. 495 (2021), p. 124719] as
n
→
∞
n \to \infty
. In this paper, we generalize and extend this result to the case where
p
p
and
q
q
have different degrees. In this case, the logarithmic potential of the limiting distribution is given by the pointwise maximum of the logarithmic potentials of
μ
\mu
and
ν
\nu
, scaled by the limiting ratio of the degrees of
p
p
and
q
q
. Additionally, our approach provides a complete description of the limiting distribution for the zeros of
p
+
q
p + q
for any pair of measures
μ
\mu
and
ν
\nu
, with different limiting behavior shown in the case when at least one of the measures fails to have a logarithmic moment.