  We study the diffusive motion of a test particle in a two-dimensional comb
structure consisting of a main backbone channel with continuously distributed
side branches, in the presence of stochastic Markovian resetting to the initial
position of the particle. We assume that the motion along the infinitely long
branches is biased by a confining potential. The crossover to the steady state
is quantified in terms of a large deviation function, which is derived for the
first time for comb structures in present paper. We show that the relaxation
region is demarcated by a nonlinear "light-cone" beyond which the system is
evolving in time. We also investigate the first-passage times along the
backbone and calculate the mean first-passage time and optimal resetting rate.
