This study examines the returns connectedness between NFTs and US sector stock markets. For this purpose, we use the recently developed technique of quantile-based regression to explore the dependence structure under various conditions. Our results support the view that connectedness between NFTs and sectoral markets is characterized by asymmetry and heterogeneity in the extreme conditions compared to the median quantile and mean-based approach. Under normal conditions, all NFTs except the ENJ are net recipients of the return spillover from the sectoral stock markets, whereas, financial, consumer staple, and industrial stocks are major net transmitters to the system. However, we observe heterogeneity at both tails, as all NFTs act as net transmitter (recipient) at the higher (lower) quantiles. This confirms the asymmetric dependence structure. We also compute the static optimal weights and hedge ratios using TVP-VAR model for the stocks/NFTs portfolios and show that investors and portfolio managers may consider including NFTs in their holdings to achieve diversification benefits.