  A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting
$\omega\colon V(G)\to\mathbb{R}$ and any list assignment $L\colon
E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling
$f$ such that $f(e)\in L(e)$ for all $e\in E(G)$, labels of edges are pairwise
distinct, and the sum of the labels on edges incident to a vertex plus the
weight of that vertex is distinct from the sum at every other vertex. In this
paper we prove that every graph on $n$ vertices having no $K_1$ or $K_2$
component is $\lfloor{\frac{4n}{3}}\rfloor$-weighted-list-antimagic.
  An oriented graph $G$ is $k$-$oriented-antimagic$ if there exists an
injective edge labeling from $E(G)$ into $\{1,\dotsc,|E(G)|+k\}$ such that the
sum of the labels on edges incident to and oriented toward a vertex minus the
sum of the labels on edges incident to and oriented away from that vertex is
distinct from the difference of sums at every other vertex. We prove that every
graph on $n$ vertices with no $K_1$ component admits an orientation that is
$\lfloor{\frac{2n}{3}}\rfloor$-oriented-antimagic.
