There's ethics/morals, then there's the law.

Legally, abandonment typically requires the owner to voluntary forsake the property and involves a positive intention to part with ownership, although some cases holds that property is also abandoned when it is involuntarily lost or left without the hope and expectation of again acquiring it. In the case of bicycles, its very difficult to know if the true owner has the intention to part ownership or whether they ever hope or expect to acquire it again. Abandoned property becomes the property of the finder, subject to the superior claim of the owner. But if its not legally abandoned, and you take it, then that is theft/larceny (criminal) or conversion (civil). However, one could argue abandonment in court but typically the defendant would have to show the intent to abandon (which can be tough...particularly if the true owner shows up). Also, there may be governmental statutes that say abandoned property on public areas belongs to the government.

Other than abandoned, property may be "lost" or "mislaid", each with their own legal definitions (although some courts have apparently disregarded the distinctions):

“Lost property” is property that the owner has involuntarily parted with through neglect, carelessness, or inadvertence and of whose whereabouts the owner has no knowledge. The finder of lost property does not acquire absolute ownership, but acquires only such property interest or right as will enable him to keep it against all the world but the rightful owner.

“Mislaid property” is property that is intentionally put into a certain place and later forgotten, and it is presumed to have been left in the custody of the owner or occupier of the premises upon which it is found; finder of mislaid property acquires no ownership rights in it, and, where such property is found upon another's premises, the finder is required to turn it over to the owner of the premises. So I'd think the bike in the apt bike room belongs to the apt owner.

Anyways, there's a lot of legal precedent on whats lost, abandoned or mislaid. This is mostly just common law; specific statutes may also apply. It doesn't seem that there is any specific legal point where one can say "that bike is definitely abandoned." Breaking locks is always a dangerous proposition as they suggest some degree of continuing ownership.

I'll stop typing now.