  The most degenerate unitary principal series representations
{\pi}_{i{\lambda},{\delta}} (with {\lambda} \in R, \delta \in Z/2Z) of G =
GL(N,R) attain the minimum of the Gelfand-Kirillov dimension among all
irreducible unitary representations of G. This article gives an explicit
formula of the irreducible decomposition of the restriction
{\pi}_{i{\lambda},{\delta}}|_H (branching law) with respect to all symmetric
pairs (G,H). For N=2n with n \geq 2, the restriction
{\pi}_{i{\lambda},{\delta}}|_H remains irreducible for H=Sp(n,R) if
{\lambda}\neq0 and splits into two irreducible representations if {\lambda}=0.
The branching law of the restriction {\pi}_{i{\lambda},{\delta}}|_H is purely
discrete for H = GL(n,C), consists only of continuous spectrum for H = GL(p,R)
\times GL(q,R) (p+q=N), and contains both discrete and continuous spectra for
H=O(p,q) (p>q\geq1). Our emphasis is laid on geometric analysis, which arises
from the restriction of `small representations' to various subgroups.
