The Minor Crossing Number of Graphs with an Excluded Minor
  The "minor crossing number" of a graph $G$ is the minimum crossing number of a graph that contains $G$ as a minor. It is proved that for every graph $H$ there is a constant $c$, such that every graph $G$ with no $H$-minor has minor crossing number at most $c|V(G)|$. 
Drago Bokal, Ga\v{s}per Fijav\v{z}, David R. Wood