I present updated compilations of both observational data and theoreti
cal predictions concerning excess line width and sizes in astrophysica
l bodies. After removing two well-known broadening mechanisms (thermal
width and width due to large scale motions such as expansion), I anal
yse statistically the excess line width W-excess. The excess line widt
h shows a changing behavior with object size R, of the form W-excess s
imilar to R(q). Taking all objects together, I find that q = 0.55 with
s.d. = 0.05. This result extends previous studies to cover 5 decades
in sizes, from 0.01 pc up to 1000 pc. Taking only objects with R < 1 p
c, I find that q = 0.7 with s.d. = 0.1, while taking only objects with
R > 1 pc gives q = 0.5 with s.d. = 0.1; thus a steeper (not flatter)
value of q at small R may be possible. Previous claims to derive a law
for objects of sizes R > 1 kpc are discussed, in relation to the prob
lem of removing obvious large scale motions from the observed line wid
th. Thus several models with predicted q values between 0 and 1 can be
eliminated, and the remaining ones could allow weak magnetic effects
on the line widths.