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Twelve years after the discovery of the Top quark, the CDF detector hascollected large samples of tt-bar events with integrated luminosities up to1-1.7 fb^-1, where we are able to probe our knowledge of the Standard Model Topquark. This article will focuss on those analysis results dedicated to find newphysics in the Top quark production: measurement of relative fractions of Toppair production mechanisms, searches for a massive resonant state decaying tott-bar pairs as well as a heavy Top-like quark decaying as the Standard ModelTop quark. Besides its production, the Top quark decay is also an interestingprobe to find Physics Beyond the Standard Model by measuring possibly anomalousvalues of the helicity fractions of the W boson in the decay t-->W(-->l+v_l)bby searching for flavour changing neutral current decays t-->Zq or by testingthe Top quark charge to be +2/3 or -4/3.

Looking for signals of New Physics in the Top quark samples with the CDF detector