```python
from typing import List, Tuple

def merge_ledgers(base: List[Tuple[str, int]], ours: List[Tuple[str, int]], theirs: List[Tuple[str, int]]) -> List[Tuple[str, int]]:
    """
    Merges three ledgers into one, combining accounts and handling deletions.
    
    :param base: The base ledger with no duplicates.
    :param ours: The first edited copy of the ledger.
    :param theirs: The second edited copy of the ledger.
    :return: The merged ledger sorted by account name.
    """
    # Validate inputs
    if not isinstance(base, list) or not isinstance(ours, list) or not isinstance(theirs, list):
        raise ValueError("All inputs must be lists.")
    
    for ledger in [base, ours, theirs]:
        for entry in ledger:
            if not isinstance(entry, tuple) or len(entry) != 2:
                raise ValueError("Each ledger entry must be a two-item tuple.")
            if not isinstance(entry[0], str) or not entry[0]:
                raise ValueError("Account name must be a non-empty string.")
            if not isinstance(entry[1], int):
                raise ValueError("Cents value must be an integer.")
    
    # Create a set of unique accounts
    accounts = set()
    for ledger in [base, ours, theirs]:
        accounts.update(entry[0] for entry in ledger)
    
    # Initialize the merged ledger
    merged_ledger = []
    
    # Process each account
    for account in accounts:
        delta_base = 0
        delta_ours = 0
        delta_theirs = 0
        
        # Calculate deltas
        for entry in base:
            if entry[0] == account:
                delta_base += entry[1]
        for entry in ours:
            if entry[0] == account:
                delta_ours += entry[1]
        for entry in theirs:
            if entry[0] == account:
                delta_theirs += entry[1]
        
        # Determine the final value for the account
        if delta_base == delta_ours == delta_theirs == 0:
            continue
        elif delta_base == delta_ours == delta_theirs:
            merged_ledger.append((account, delta_base))
        elif delta_base == delta_ours:
            merged_ledger.append((account, delta_base + delta_theirs))
        elif delta_base == delta_theirs:
            merged_ledger.append((account, delta_base + delta_ours))
        elif delta_ours == delta_theirs:
            merged_ledger.append((account, delta_ours + delta_base))
        else:
            merged_ledger.append((account, delta_base + delta_ours + delta_theirs))
    
    # Sort the merged ledger by account name
    merged_ledger.sort(key=lambda x: x[0])
    
    return merged_ledger
```