```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 False:
            continue
        if name in held:
            held[name] = tick
            renders.append((tick, name))
        elif len(held) == size:
            oldest_name, oldest_tick = min(held.items(), key=lambda x: (x[1], x[0]))
            del held[oldest_name]
            held[name] = tick
            renders.append((tick, name))
        else:
            held[name] = tick
            renders.append((tick, name))
    return renders
```