  We consider a triple-quantum-dot (TQD) system composed by an interacting
quantum dot connected to two effectively non-interacting dots, which in turn
are both connected in parallel to metallic leads. As we show, this system can
be mapped onto a single-impurity Anderson model with a non-trivial density of
states. The TQD's transport properties are investigated under a continuous
tuning of the non-interacting dots' energy-levels, employing the Numerical
Renormalization Group technique. Interference between single and many-particle
resonances splits the Kondo peak, fulfilling a generalized Friedel sum rule. In
addition, a particular configuration in which one of the non-interacting dots
is held out of resonance with the leads allows to access a pseudogap regime
where a Kosterlitz-Thouless type quantum-phase-transition (QPT) occur,
separating the Kondo and non-Kondo behavior. Within this same configuration,
the TQD exhibits traces of the Fano-Kondo effect, which is in turn, strongly
affected by the QPT. Signatures of all these phenomena are neatly displayed by
the calculated linear conductance.
