  A detailed analysis of the Kondo effect of a magnetic impurity in a zigzag
graphene nanoribbon is addressed. An adatom is coupled to the graphene
nanoribbon via a hybridization amplitude $\Gamma_{imp}$ in a hollow or top site
configuration. In addition, the adatom is also weakly coupled to a metallic STM
tip by a hybridization function $\Gamma_{tip}$ that provides a Kondo screening
of its magnetic moment. The entire system is described by an Anderson-like
Hamiltonian whose low-temperature physics is accessed by employing the
numerical renormalization group approach, which allows us to obtain the
thermodynamic properties used to compute the Kondo temperature of the system.
We find two screening regimes when the adatom is close to the edge of the
zigazag graphene nanoribbon: (1) a weak coupling regime ($\Gamma_{imp}\ll
\Gamma_{tip}$), in which the edge states produce an enhancement of the Kondo
temperature $T_K$ and (2) a strong coupling regime ($\Gamma_{imp}\gg
\Gamma_{tip}$), in which a local singlet is formed, in detriment to the Kondo
screening by the STM tip. These two regimes can be clearly distinguished by the
dependence of their characteristic temperature $T^*$ on the coupling between
the adatom and the carbon sites of the graphene nanoribon ($V_{imp}$). We
observe that in the weak coupling regime $T^*$ increases exponentially with
$V_{imp}^2$. Differently, in the strong coupling regime, $T^*$ increases
linearly with $V_{imp}^2$.
