Is there a term to quantify how spread a character is on a phylogenetic tree?
I agree with Terdon's terminology in the comment ("ubiquitous" or "widespread").

You can use clade-specific or species-specific for a restricted character.

For the characters that appear in all species of a branch and in a quantitative way you can also provide the estimated age of the last common ancestor to the branch featuring that character. This tool might help you: http://www.timetree.org/