Inclusion Criteria:  Body weight >= 5 kg at screening. Vaccination against Neisseria meningitidis. For participants receiving other therapies (e.g., immunosuppressants, corticosteroids, mTORi, or calcineurin inhibitors: stable dose for >= 28 days. For female participants of childbearing potential: an agreement to remain abstinent or use contraception. Participants with a prior kidney transplant are eligible if they have a known history of complement-mediated aHUS prior to the kidney transplant. Evidence of TMA (for Naive Cohort only). Onset of TMA =<28 days prior to first crovalimab administration (for Naive Cohort and participants in the Pretreated Cohort with TMA present at the time of screening). Documented treatment with a C5 inhibitor (for Switch Cohort only). Clinical evidence of response to a C5 inhibitor (for Switch Cohort only). Poorly controlled TMA following treatment with another C5 inhibitor (for C5 SNP participants in the Pretreated Cohort only). Known C5 polymorphism (for C5 SNP participants in the Pretreated Cohort only).  Exclusion Criteria:  TMA associated with non-aHUS related renal disease. Positive direct Coombs test. Chronic dialysis and/or end stage renal disease. Identified drug exposure-related TMA. Presence or history of a condition that could trigger TMA, such as malignancy, organ transplant (other than kidney transplant) or autoimmune disease. History of a kidney disease, other than aHUS. History of Neisseria meningitidis infection within 6 months. Known or suspected immune deficiency (e.g., history of frequent recurrent infections). Positive HIV test. Multi-system organ dysfunction or failure. Recent IVIg treatment. Pregnant or breastfeeding or intending to become pregnant. Participation in another interventional treatment study with an investigational agent or use of any experimental therapy within 28 days of screening or within five half lives of that investigational product, whichever is greater. Recent use of tranexamic acid. Current or previous treatment with a complement inhibitor (for Naive Cohort only). Positive for Active Hepatitis B and/or C infections (HBV/HCV) (for Switch Cohort and switching C5 SNP Pretreated Cohort participants who recently received C5 inhibitor treatment). Cryoglobulinemia at screening (for Switch Cohort and C5 SNP Cohort participants who recently received C5 inhibitor treatment). Documented condition leading to non-aHUS TMA: Thrombotic Thrombocytopenic Purpura (TTP), Shiga Toxin producing Escherichia Coli (STEC)-TMA, Pneumococcal HUS, TMA secondary to cobalamin C defect and TMA related to Diacylglycerol kinase ε (DGKE) nephropathy.