No, you don't directly own cryptocurrency when you invest in a crypto ETP. Instead, you own shares in a financial instrument that tracks the performance of the underlying cryptocurrency.
Here's how it works: The ETP provider (like BlackRock or VanEck) holds the actual cryptocurrency in secure custody, and you own a share of that ETP, which gives you exposure to the cryptocurrency's price movements. This is similar to how an ETF works - you don't own the individual stocks in the index, but you benefit from their performance.
This structure provides several features: you get cryptocurrency exposure without needing to manage wallets or private keys, benefit from institutional-grade security, and can easily buy and sell through familiar investment platforms.