  According to a generic temperature vs. carrier-doping (T-p) phase diagram of
high-temperature superconductors it has been proposed that as doping increases
to the overdoped region they approach gradually a conventional (canonical)
Fermi Liquid. However, Hall effect measurements in several systems reported by
different authors show a still strong \emph{T}-dependence in overdoped samples.
We report here electrical transport measurements of
Y_{1-x}Ca_{x}Ba_{2}Cu_{3}O_{7-delta} thin films presenting a temperature
dependence of the Hall constant, R_H, which does not present a gradual
transition towards the T-independent behavior of a canonical Fermi Liquid.
Instead, the T-dependence passes by a minimum near optimal doping and then
increases again in the overdoped region. We discuss the theoretical predictions
from two representative Fermi Liquid models and show that they can not give a
satisfactory explanation to our data. We conclude that this region of the phase
diagram in YBCO, as in most HTSC, is not a canonical Fermi Liquid, therefore we
call it Anomalous Fermi Liquid.
