```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:
            renders.append([tick, name])
        else:
            held[tick] = name
            renders.append([tick, name])
            if len(held) > size:
                oldest_key = min(held, key=lambda x: held[x])
                del held[oldest_key]
    return renders
```