  We apply the general relativistic resistive magnetohydrodynamics code {\tt
BHAC} to perform a 2D study of the formation and evolution of a reconnection
layer in between two merging magnetic flux tubes in Minkowski spacetime.
Small-scale effects in the regime of low resistivity most relevant for dilute
astrophysical plasmas are resolved with very high accuracy due to the extreme
resolutions obtained with adaptive mesh refinement. Numerical convergence in
the highly nonlinear plasmoid-dominated regime is confirmed for a sweep of
resolutions. We employ both uniform resistivity and non-uniform resistivity
based on the local, instantaneous current density. For uniform resistivity we
find Sweet-Parker reconnection, from $\eta = 10^{-2}$ down to $\eta = 10^{-4}$,
for a reference case of magnetisation $\sigma = 3.33$ and plasma-$\beta = 0.1$.
{For uniform resistivity $\eta=5\times10^{-5}$ the tearing mode is recovered,
resulting in the formation of secondary plasmoids. The plasmoid instability
enhances the reconnection rate to $v_{\rm rec} \sim 0.03c$ compared to $v_{\rm
rec} \sim 0.01c$ for $\eta=10^{-4}$.} For non-uniform resistivity with a base
level $\eta_0 = 10^{-4}$ and an enhanced current-dependent resistivity in the
current sheet, we find an increased reconnection rate of $v_{\rm rec} \sim
0.1c$. The influence of the magnetisation $\sigma$ and the plasma-$\beta$ is
analysed for cases with uniform resistivity $\eta=5\times10^{-5}$ and
$\eta=10^{-4}$ in a range $0.5 \leq \sigma \leq 10$ and $0.01 \leq \beta \leq
1$ in regimes that are applicable for black hole accretion disks and jets. The
plasmoid instability is triggered for Lundquist numbers larger than a critical
value of $S_{\rm c} \approx 8000$.
