```ts
/** Replay tile requests against a size-limited cache of fresh renders. */
export function tileRenders(requests: [number, string][], freshFor: number, size: number): [number, string][] {
  if (!Number.isInteger(freshFor) || freshFor < 1 || !Number.isInteger(size) || size < 1) {
    throw new Error("freshFor and size must be positive integers");
  }
  const held = new Map<string, { tick: number, name: string }>();
  const renders: [number, string][] = [];
  for (const [tick, name] of requests) {
    if (tick < freshFor) {
      // Serve a still-fresh render
      const cachedRender = held.get(name);
      if (cachedRender && cachedRender.tick >= tick) {
        renders.push([tick, name]);
      } else {
        // Make room when full and record one
        if (held.size === size) {
          const oldestEntry = Array.from(held.entries()).reduce((oldest, [_, aName, { tick: atick }]) => 
            atick < oldest.tick ? [aName, atick] : oldest, [null, -Infinity]);
          held.delete(oldestEntry[0]);
        }
        held.set(name, { tick, name });
        renders.push([tick, name]);
      }
    } else {
      // Record a new render
      held.set(name, { tick, name });
      renders.push([tick, name]);
    }
  }
  return renders;
}
```