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The question of how supermassive black holes (SMBHs) grow over cosmic time isa major puzzle in high-energy astrophysics. One promising approach to thisproblem is via the study of tidal disruption flares (TDFs). These are transientevents resulting from the disruption of stars by quiescent supermassive blackholes at centers of galaxies. A meter-class X-ray observatory with a timeresolution $\sim$ a millisecond and a spectral resolution of a few eV at KeVenergies would be revolutionary as it will facilitate high signal to noisespectral-timing studies of several cosmological TDFs. It would open a new eraof astrophysics where SMBHs in TDFs at cosmic distances can be studied insimilar detail as current studies of much nearer, stellar-mass black holebinaries. Using Athena X-ray observatory as an example, we highlight twospecific aspects of spectral-timing analysis of TDFs. (1) Detection of X-rayquasi-periodic oscillations (QPOs) over a redshift range and using these signalfrequencies to constrain the spin evolution of SMBHs, and (2) Time-resolvedspectroscopy of outflows/winds to probe super-Eddington accretion. SMBH spindistributions at various redshifts will directly allow us to constrain theirprimary mode of growth as higher spins are predicted due to spin-up forprolonged accretion-mode growth, while lower spins are expected for growth viamergers due to angular momentum being deposited from random directions. Ameter-class X-ray telescope will also be able to characterize relativisticTDFs, viz., SwJ1644+57-like events, out to a redshift greater than 8, i.e., itwould facilitate detailed spectral-timing studies of TDFs by the youngest SMBHsin the Universe.

Probing the Cosmological Evolution of Super-massive Black Holes using Tidal Disruption Flares