  The duration of orbital decay induced by gravitational waves (GWs) is often
the bottleneck of the evolutionary phases going from star formation to a
merger. We show here that kicks imparted to the newly born compact object
during the second collapse generically result in a GW merger time distribution
behaving like $dN/d\log t \propto t^{2/7}$ at short durations, leading to
ultrafast mergers. Namely, a nonnegligible fraction of neutron star binaries,
formed in this way, will merge on a time scale as short as 10 Myr, and a small
fraction will merge even on a time scale less than 10 kyr. The results can be
applied to different types of compact binaries. We discuss here the
implications for binary neutron star mergers. These include unique short
gamma-ray bursts (GRBs), eccentric and misaligned mergers, $r$-process
enrichment in the very early Universe and in highly star-forming regions, and
possible radio precursors. Interestingly, we conclude that among the few
hundred short GRBs detected so far, a few must have formed via this ultrafast
channel.
