What nation withdrew from the british Commonwealth to form an independent republic

Republic? The United States of America, often described as a democracy, is actually a republic.

Withdrawing from the British commonwealth itself?

US, India, large portions of Africa, now a variety of different countries, Canada, Australia (The land of the criminals), New Zealand, areas of South East Asia seized by the Japanese ... It's quite a volatile rise and fall. At it's peak, the English Empire controlled about 20% of the population of the world.