Preposition for islands: “auf Venedig”,…, “auf Grönland”?

Question

I was surprised to hear

auf Kuba

For islands one uses auf but I somehow assumed "very small Islands" was the scope of that use.

Greenland is the largest island you can find. Do we also have to say

auf Grönland

or in Grönland as here reads?

Eriks Beschreibung der Insel war allerdings ein wenig geschönt. In Grönland gibt es zwar Küstenregionen, die im arktischen Sommer von saftigem, grünem Weideland überzogen sind. ^{Planet Wissen}

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I also assume automatically one doesn't say auf Australien, since Australia is no longer precisely an island. Rapid search renders results, but the combination auf Australien appears to have another context, though.

Answer 1

Auf is and should be used for islands of any kind, as long as you’re talking about the island being an island.

Als wir auf Grönland an Land gegangen sind, …
Auf der Herreninsel steht ein Königsschloss.
Auf Malta kommen immer wieder Flüchtligsschiffe an.
Auf Kuba gibt es gute Zigarren.
Auf Lummerland gibt es zwei Berge, viele Tunnels und Gleise.

In is and should be used for countries of any kind, and also for expressing stuff that implies the thing you’re talking about is a country.

In Kuba herrscht seit gut fünfzig Jahren die »ewige Revolution«.
In Malta kann man sich die Staatsbürgerschaft kaufen.
In Lummerland heißt der König Alfons der viertel-vor-zwölfte.
In Neuseeland wurde der Herr der Ringe gedreht.
In England und in Irland wird auf der linken Straßenseite gefahren.

Taking the case of England and Ireland: Technically these are generalised names meaning Great Britain and Ireland (the island, not the republic) respectively. However, they are often also understood to mean England (not Scotland or Wales) and the Republic of Ireland, which disqualifies the use of auf, because both entities are not composed of one entire island.

Taking the case of New Zealand, I would use in when speaking about the country, i. e. both islands, while I would say auf der Nord-/Südinsel.

Cuba and Malta seem to work differently well with in in my ears; all examples I was trying to think of immediately suggested auf, but I’m fine with saying in the way I did just now.

Auf Haiti is wrong, though, because there’s also the Dominican Republic on the other half of the island Hispaniola. Auf Hispaniola works, while in Hispaniola is, of course, wrong.

Australia is considered a continent or a country, never an island. So even if you’re speaking about the islandic properties, use in:

Nur in Australien gibt es Kängurus.

Venice is not considered an island and thus uses in exclusively. Lindau, however, is both the name of the island and the name of the town, so auf Lindau expresses that you’re talking about the island borough of Lindau.

Answer 2

Auf can be used with all islands, even somewhat larger ones: auf Sylt, auf Malta, auf Madagaskar ... You can always use in for countries proper, however, regardless of their being an island, i.e. in Kuba is perfectly fine. In Grönland sounds fine, too, to my native ears. Auf Venedig, however, does not: there's not a single island by that name, as the City of Venice is spread out over multiple smaller islands.

I don't think anybody would say auf Australien, though, you're correct. For New Zealand, on the other hand, I have auf seen used.