```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 0:
            raise ValueError("tick must be monotonic")
        if name in held:
            if tick - held[name] < fresh_for:
                renders.append((tick, name))
                held[name] = tick
            else:
                del held[name]
                renders.append((tick, name))
        else:
            if len(held) >= size:
                oldest = min(held, key=lambda k: held[k])
                del held[oldest]
                renders.append((tick, oldest))
            held[name] = tick
            renders.append((tick, name))
    return renders
```