By the time we reach Communism, that is, the Marxist vision of a fully publicly owned and planned world economy, distribution of wealth will likely be based on need. There is no necessity for equal wealth, as humans have very unequal needs. Equal ownership of property is certified through public ownership.

If you're asking what's preventing someone from starting a business, it would be the sheer difficulties of actually starting one that can compete with the highly developed productive forces in the rest of the economy. Communism isn't so much about outlawing private property, as developing beyond it.