```ts
export function splitCents(total: number, weights: number[]): number[] {
  if (!Number.isInteger(total)) throw new Error("total must be whole cents");
  if (total < 0) throw new Error("total may not be negative");
  if (!Array.isArray(weights) || weights.length === 0) throw new Error("weights must be a non-empty list");
  if (!weights.every((w) => Number.isInteger(w) && w > 0)) throw new Error("a weight is a positive whole number");

  const whole = weights.reduce((a, b) => a + b, 0);
  const parts = weights.map((w) => Math.floor((total * w) / whole));
  let remainingCents = total - parts.reduce((a, b) => a + b, 0);

  const fractions = weights.map((w, i) => ({
    index: i,
    fraction: (total * w) % whole
  }));

  fractions.sort((a, b) => {
    if (b.fraction === a.fraction) return a.index - b.index;
    return b.fraction - a.fraction;
  });

  for (const { index } of fractions) {
    if (remainingCents > 0) {
      parts[index]++;
      remainingCents--;
    }
  }

  return parts;
}
```