  The diffusion process of N hard rods in a 1D interval of length L (--> inf)
is studied using scaling arguments and an asymptotic analysis of the exact
N-particle probability density function (PDF). In the class of such systems,
the universal scaling law of the tagged particle's mean absolute displacement
reads, <|r|>~ <|r|>_{free}/n^mu, where <|r|>_{free} is the result for a free
particle in the studied system and n is the number of particles in the covered
length. The exponent mu is given by, mu=1/(1+a), where a is associated with the
particles' density law of the system, rho~rho_0*L^(-a), 0<= a <=1. The scaling
law for <|r|> leads to, <|r|>~rho_0^((a-1)/2) (<|r| >_{free})^((1+a)/2), an
equation that predicts a smooth interpolation between single file diffusion and
free particle diffusion depending on the particles' density law, and holds for
any underlying dynamics. In particular, <|r|>~t^((1+a)/2) for normal diffusion,
with a Gaussian PDF in space for any value of a (deduced by a complementary
analysis), and, <|r|>~t^((beta(1+a))/2), for anomalous diffusion in which the
system's particles all have the same power-law waiting time PDF for individual
events, psi~t^(-1-beta), 0<beta<1. Our analysis shows that the scaling
<|r|>~t^(1/2) in a 'standard' single file is a direct result of the fixed
particles' density condition imposed on the system, a=0.
