  We present electrical resistivity and specific heat measurements of alloys on
the Rh rich side of the phase diagram of the Ce(Rh$_{1-x}$Pd$_x$)$_2$Si$_2$
system and compare the results with those obtained at intermediate and low Rh
concentrations. The analysis of the x-evolution of the entropy and the scaling
behaviour of $C_{el}(T)$ and $\rho(T)$ clearly confirm a separation of the
magnetic phase diagram into two regions. The region $x\le0.3$, showing a
concentration independent characteristic temperature $T_o\approx45 {\rm K}$,
while for $x>0.3$ $T_o$ decreases down to $T_o(x=1)\approx15 {\rm K}$. This
characteristic temperature is obtained by scaling the $C_{el}(T,x>0.3)$ results
as a function of the reduced temperature $T/T_o$. At low Pd-content, $T_N$
decreases very rapidly from $T_N = 36 {\rm K}$ in pure CeRh$_2$Si$_2$ to
$T_N=18 {\rm K}$ at x=0.1. With higher Pd concentration it stabilized at
$T_N\approx15 {\rm K}$ whereas the magnitude of the anomalies in $C_{el}(T)$
and in the susceptibility around $T_N$ are further reduced and disappear at
$x\approx0.3$. This is in contrast to the behavior found on the Pd-rich side,
where $T_N$ decreases continuously to zero with increasing Rh content. The
pronounced differences observed between both phase boundaries and the drastic
effect of doping on the Rh rich side suggest an itinerant character in CeRh$_2$
Si$_2$, in contrast to the localized character of CePd$_2$Si$_2$. A further
evidence for the itinerant character in CeRh$_2$Si$_2$ is given by the
$\rho(T)$ dependence observed for $x\le0.3$, which scales with $\rho(T)$ of the
prototype itinerant compound YCo$_2$.
