```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 in held and tick + fresh_for > len(renders):
            renders.append([tick, name])
            del held[tick]
            held[tick] = name
        elif len(held) >= size:
            oldest_key = min(held, key=lambda k: (held[k], k))
            del held[oldest_key]
            del renders[renders.index([oldest_key, held[oldest_key]])]
            renders.append([tick, name])
            held[tick] = name
        else:
            renders.append([tick, name])
            held[tick] = name
    return renders
```