```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 < renders[-1][0] if renders else None:
            continue
        if name in held:
            if tick - held[name][0] >= fresh_for:
                del held[name]
        else:
            if len(held) == size:
                oldest_name = min(held, key=lambda x: held[x][0])
                del held[oldest_name]
        held[name] = tick
        renders.append([tick, name])
    return renders
```