  We address the problem of the percolative phase separation in polycrystalline
samples of Pr$_{0.5-\delta}$Ca$_{0.2+\delta}$Sr$_{0.3}$MnO$_3$ for $-0.04\leq
\delta \leq 0.04$ (hole doping $n$ between 0.46 and 0.54). We perform
measurements of X-ray diffraction, dc magnetization, ESR, and electrical
resistivity. These samples show at $T_C$ a paramagnetic (PM) to ferromagnetic
(FM) transition, however, we found that for $n>0.50$ there is a coexistence of
both of these phases below $T_C$. On lowering $T$ below the charge-ordering
(CO) temperature $T_{CO}$ all the samples exhibit a coexistence between the FM
metallic and CO (antiferromagnetic) phases. In the whole $T$ range the FM phase
fraction ($X$) decreases with increasing $n$. Furthermore, we show that only
for $n\leq 0.50$ the metallic fraction is above the critical percolation
threshold $X_C\simeq 15.5%$. As a consequence, these samples show very
different magnetoresistance properties. In addition, for $n\leq 0.50$ we
observe a percolative metal-insulator transition at $T_{MI}$, and for
$T_{MI}<T<T_{CO}$ the insulating-like behavior generated by the enlargement of
$X$ with increasing $T$ is well described by the percolation law $\rho
^{-1}=\sigma \sim (X-X_C)^t$, where $t$ is a critical exponent. On the basis of
the values obtained for this exponent we discuss different possible percolation
mechanisms, and suggest that a more deep understanding of geometric and
dimensionality effects is needed in phase separated manganites. We present a
complete $T$ vs $n$ phase diagram showing the magnetic and electric properties
of the studied compound around half doping.
