The CO2 removal model inter-comparison (CDRMIP) has been established to approximate the usefulness of climate mitigation by some well-defined negative emission technologies. I here analyze ocean alkalinization in a high CO2 world (emission scenario SSP5-85-EXT++ and CDR-ocean-alk within CDRMIP) for the next millennia using a revised version of the carbon cycle model BICYCLE, whose long-term feedbacks are calculated for the next 1 million years. The applied model version not only captures atmosphere, ocean, and a constant marine and terrestrial biosphere, but also represents solid Earth processes, such as deep ocean CaCO3 accumulation and dissolution, volcanic CO2 outgassing, and continental weathering. In the applied negative emission experiment, 0.14 Pmol/yr of alkalinity—comparable to the dissolution of 5 Pg of olivine per year—is entering the surface ocean starting in year 2020 for either 50 or 5000 years. I find that the cumulative emissions of 6,740 PgC emitted until year 2350 lead to a peak atmospheric CO2 concentration of nearly 2,400 ppm in year 2326, which is reduced by only 200 ppm by the alkalinization experiment. Atmospheric CO2 is brought down to 400 or 300 ppm after 2730 or 3480 years of alkalinization, respectively. Such low CO2 concentrations are reached without ocean alkalinization only after several hundreds of thousands of years, when the feedbacks from weathering and sediments bring the part of the anthropogenic emissions that stays in the atmosphere (the so-called airborne fraction) below 4%. The efficiency of carbon sequestration by this alkalinization approach peaks at 9.7 PgC per Pmol of alkalinity added during times of maximum anthropogenic CO2 emissions and slowly declines to half this value 2000 years later due to the non-linear marine chemistry response and ocean-sediment processes. In other words, ocean alkalinization sequesters carbon only as long as the added alkalinity stays in the ocean. To understand the basic model behavior, I analytically explain why in the simulation results a linear relationship in the transient climate response (TCR) to cumulative emissions is found for low emissions (similarly as for more complex climate models), which evolves for high emissions to a non-linear relation.