It didn't the US was formed when it revolted against the British Empire
In reality, Bermuda did not actually choose to join the British Empire. They islands were forced to join or be conquered.
The U S A never joined the British Empire.
1894
1878
Canada didnt join it was fought over by the French and British in which the Brits ended up winning therefore becoming part of her empire.
1964
For who?
China never joined the British Empire. However, two small parts of China were part of the British Empire. Weihaiwei-1898-1930 Hong Kong-1841-1997
Scotland, Ireland Wales.
Most of them had no choice because they were conquered militarily.
Australia did not 'join' the British Empire, the British was the first westerners who set foot on Australia. They stuck the Union Jack down, and claimed Australia as theirs.
Well you have not told us which Empire you are asking about or what "it" was. However, as the British Empire was the largest in history, it is probable that whatever "it" was it split from the British Empire.