Short answer. The owner of the principal thing. Article 466 of the Civil Code provides that when two movable things belonging to different owners are united without bad faith into a single object, the owner of the principal thing acquires the accessory — but must indemnify the accessory's previous owner for its value.
What the law says
Whenever two movable things belonging to different owners are, without bad faith, united in such a way that they form a single object, the owner of the principal thing acquires the accessory, indemnifying the former owner thereof for its value.
Civil Code, Article 466 — Adjunction (Conjunction). Read the full provision →
The principal absorbs the accessory
Article 466 states that whenever two movable things belonging to different owners are, without bad faith, united in such a way that they form a single object, the owner of the principal thing acquires the accessory. Once the two items are genuinely combined into one object — not merely placed side by side, but joined so they function or exist as a single thing — ownership of the whole vests in whoever owned the more important of the two components. The other owner's separate title to their contribution is absorbed into that single ownership.
Ownership comes with a price, not a windfall
The article does not let the owner of the principal thing keep the accessory for free: they must be indemnifying the former owner thereof for its value. So the rule is not simply "the bigger or more valuable item wins outright" — it resolves what happens to the physical object while still requiring payment to the person who lost separate ownership of their component. The former owner of the accessory ends up compensated, even though they no longer own a separate thing.
Why "without bad faith" matters here
Article 466's rule is expressly limited to a union that happens without bad faith. That qualifier signals that the outcome is different when one owner deliberately or dishonestly caused the joining, though this article does not itself spell out what that different outcome looks like. If bad faith is part of your situation, this specific provision is not the one governing it, and the answer would depend on rules this article does not cover.
What Article 466 leaves open
The article does not define, within its own text, what makes one of the two things "the principal" rather than the accessory. That determination is left to be made under whatever criteria separately govern the distinction, so identifying which of your two items is legally the principal thing is a necessary step this article assumes has already been answered rather than one it walks through itself.