  We present analytical results for the distribution of cover times of random
walks (RWs) on random regular graphs consisting of $N$ nodes of degree $c$ ($c
\ge 3$). Starting from a random initial node at time $t=1$, at each time step
$t \ge 2$ an RW hops into a random neighbor of its previous node. In some of
the time steps the RW may visit a new, yet-unvisited node, while in other time
steps it may revisit a node that has already been visited before. The cover
time $T_{\rm C}$ is the number of time steps required for the RW to visit every
single node in the network at least once. We derive a master equation for the
distribution $P_t(S=s)$ of the number of distinct nodes $s$ visited by an RW up
to time $t$ and solve it analytically. Inserting $s=N$ we obtain the cumulative
distribution of cover times, namely the probability $P(T_{\rm C} \le t) =
P_t(S=N)$ that up to time $t$ an RW will visit all the $N$ nodes in the
network. Taking the large network limit, we show that $P(T_{\rm C} \le t)$
converges to a Gumbel distribution. We calculate the distribution of partial
cover (PC) times $P( T_{{\rm PC},k} = t )$, which is the probability that at
time $t$ an RW will complete visiting $k$ distinct nodes. We also calculate the
distribution of random cover (RC) times $P( T_{{\rm RC},k} = t )$, which is the
probability that at time $t$ an RW will complete visiting all the nodes in a
subgraph of $k$ randomly pre-selected nodes at least once. The analytical
results for the distributions of cover times are found to be in very good
agreement with the results obtained from computer simulations.
