```python
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])
            held[tick] = name
        elif len(held) >= size:
            oldest_tick = min(held)
            del held[oldest_tick]
            renders.append([tick, name])
            held[tick] = name
    return renders
```