```typescript
/** 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 && held.has(name)) {
      // Serve a still-fresh render
      const entry = held.get(name)!;
      if (entry.tick + freshFor > tick) {
        renders.push([tick, name]);
      }
    } else {
      // Make room when full and record one
      while (held.size >= size && !held.isEmpty()) {
        held.delete([...held.keys()][0]); // Drop the oldest entry
      }

      if (!held.has(name)) {
        held.set(name, { tick, name });
      }

      renders.push([tick, name]);
    }
  }

  return renders;
}
```