If border control refuses me entry at the airport, can I fly to any chosen country or only the country of origin?

The scenario:

a person is flying from country A to country B
upon landing, they are refused entry to the country B by the border control

question: instead of flying back to A, can they book the next flight to a country C and fly there?

EDIT: I was asked to make the scenario more specific, so:

Let's say a citizen of Hong Kong wants to go on a trip to Europe. They chose UK as the first country they will visit.

Hong Kong is a "Special Administrative Region", therefore they do not require a visa to enter the UK, yet border control decides to refuse entry (for whatever reason, but let's assume the traveler did nothing illegal).

The traveler doesn't want to waste his holidays and go back home disappointed. Can he now chose to take a flight to a different European country, such as Germany? (they don't need a visa there either thanks to a visa-waiver program)

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If border control refuses me entry at the airport, can I fly to any chosen country or only the country of origin? - Closeup of map of Africa with countries borders and water on sunny day

If border control refuses me entry at the airport, can I fly to any chosen country or only the country of origin? - Top view of paper world map with continents and different countries oceans and seas placed in sunny room

What happens if you fly to a country and are denied entry?

If you are denied entry by US Immigration, the airline is responsible to fly you back to your country of origin - or at least wherever your arriving flight came from.

What happens if you are denied entry at airport?

Many foreign travelers are denied entry to the US at airport terminals every day. When you get to the airline counter, three things could happen: They apply your return ticket to your flight back. They add a fee to change your return flight date.

What happens if you are refused entry at the border?

After the denial of entry, the American border will often contact the RCMP and let them know the whereabouts of the wanted person. If the warrant is stateside, instead of receiving a refusal of entry the individual will likely be arrested on the spot.

Can countries refuse entry?

Some sovereign states refuse entry to all citizens of certain states. These restrictions differ from travel visa requirements, which require travelers to obtain permission to enter a country in advance of their travel.

These Countries will DENY ENTRY at Immigration. Vacation Disasters

Sources: Stack Exchange - This article follows the attribution requirements of Stack Exchange and is licensed under CC BY-SA 3.0.

Images: Atypeek Dgn, vectors icon, Nothing Ahead, Nothing Ahead