  The question of how supermassive black holes (SMBHs) grow over cosmic time is
a major puzzle in high-energy astrophysics. One promising approach to this
problem is via the study of tidal disruption flares (TDFs). These are transient
events resulting from the disruption of stars by quiescent supermassive black
holes at centers of galaxies. A meter-class X-ray observatory with a time
resolution $\sim$ a millisecond and a spectral resolution of a few eV at KeV
energies would be revolutionary as it will facilitate high signal to noise
spectral-timing studies of several cosmological TDFs. It would open a new era
of astrophysics where SMBHs in TDFs at cosmic distances can be studied in
similar detail as current studies of much nearer, stellar-mass black hole
binaries. Using Athena X-ray observatory as an example, we highlight two
specific aspects of spectral-timing analysis of TDFs. (1) Detection of X-ray
quasi-periodic oscillations (QPOs) over a redshift range and using these signal
frequencies to constrain the spin evolution of SMBHs, and (2) Time-resolved
spectroscopy of outflows/winds to probe super-Eddington accretion. SMBH spin
distributions at various redshifts will directly allow us to constrain their
primary mode of growth as higher spins are predicted due to spin-up for
prolonged accretion-mode growth, while lower spins are expected for growth via
mergers due to angular momentum being deposited from random directions. A
meter-class X-ray telescope will also be able to characterize relativistic
TDFs, viz., SwJ1644+57-like events, out to a redshift greater than 8, i.e., it
would facilitate detailed spectral-timing studies of TDFs by the youngest SMBHs
in the Universe.
