  We explore the ability of future low-frequency gravitational wave detectors
to measure the spin of stellar mass and intermediate mass black holes that
inspiral onto super-massive Kerr black holes (SMBHs). We develop a kludge
waveform model based on the equations of motion derived by Saijo et al. [Phys
Rev D 58, 064005, 1998] for spinning BH binaries, augmented with spin-orbit and
spin-spin couplings taken from perturbative and post-Newtonian (PN)
calculations, and the associated conservative self-force corrections, derived
by comparison to PN results. We model the inspiral phase using accurate fluxes
which include perturbative corrections for the spin of the inspiralling body,
spin-spin couplings and higher-order fits to solutions of the Teukolsky
equation. We present results of Monte Carlo simulations of parameter estimation
errors and of the model errors that arise when we omit conservative corrections
from the waveform template. For a source 5000+10^6 solar mass observed with an
SNR of 1000, LISA will be able to determine the two masses to within a
fractional error of ~0.001, measure the SMBH spin magnitude, q, and the spin
magnitude of the inspiralling BH to 0.0001, 10%, respectively, and determine
the location of the source in the sky and the SMBH spin orientation to within
0.0001 steradians. For a 10+10^6 solar mass system observed with SNR of 30,
LISA will not be able to determine the spin magnitude of the inspiralling BH,
although the measurement of the other waveform parameters is not significantly
degraded by the presence of spin. The model errors which arise from ignoring
conservative corrections become significant for mass-ratios above 0.0001, but
including these corrections up to 2PN order may be sufficient to reduce these
systematic errors to an acceptable level.
