  We compare the science capabilities of different eLISA mission designs,
including four-link (two-arm) and six-link (three-arm) configurations with
different arm lengths, low-frequency noise sensitivities and mission durations.
For each of these configurations we consider a few representative massive black
hole formation scenarios. These scenarios are chosen to explore two physical
mechanisms that greatly affect eLISA rates, namely (i) black hole seeding, and
(ii) the delays between the merger of two galaxies and the merger of the black
holes hosted by those galaxies. We assess the eLISA parameter estimation
accuracy using a Fisher matrix analysis with spin-precessing, inspiral-only
waveforms. We quantify the information present in the merger and ringdown by
rescaling the inspiral-only Fisher matrix estimates using the signal-to-noise
ratio from non-precessing inspiral-merger-ringdown phenomenological waveforms,
and from a reduced set of precessing numerical relativity/post-Newtonian hybrid
waveforms. We find that all of the eLISA configurations considered in our study
should detect some massive black hole binaries. However, configurations with
six links and better low-frequency noise will provide much more information on
the origin of black holes at high redshifts and on their accretion history, and
they may allow the identification of electromagnetic counterparts to massive
black hole mergers.
