```python
"""Replay tile requests against a size-limited cache of fresh renders."""


def tile_renders(requests: list, fresh_for: int, size: int) -> list:
    for count in (fresh_for, size):
        if isinstance(count, bool) or not isinstance(count, int) or count < 1:
            raise ValueError("fresh_for and size must be positive integers")
    held = {}
    renders = []
    for tick, name in requests:
        if tick <= max(held.keys()) + fresh_for:
            continue
        while len(held) >= size:
            oldest_name = min(held, key=lambda k: (held[k][0], held[k][1]))
            del held[oldest_name]
        held[name] = (tick, name)
        renders.append([tick, name])
    return renders
```