  The decay rate of late time tails in the Kerr spacetime have been the cause
of numerous conflicting results, both analytical and numerical. In particular,
there is much disagreement on whether the decay rate of an initially pure
multipole moment ${\ell}$ is according to $t^{-(2{\bar\ell}+3)}$, where
${\bar\ell}$ is the least multipole moment whose excitation is not disallowed,
or whether the decay rate is according to $t^{-n}$, where $n=n({\ell})$. We do
careful 2+1D numerical simulations, and explain the various results. In
particular, we show that pure multipole outgoing initial data in either
Boyer--Lindquist on ingoing Kerr coordinates on the corresponding slices lead
to the same late time tail behavior. We also show that similar initial data
specified in terms of the Poisson spherical coordinates lead to the simpler
$t^{-(2{\bar\ell}+3)}$ late time tail. We generalize the rule $n=n({\ell})$ to
subdominant modes, and also study the behavior of non--axisymmetric initial
data. We discuss some of the causes for possible errors in 2+1D simulations,
demonstrate that our simulations are free of those errors, and argue that some
conflicting past results may be attributed to them.
