This paper examines crosscountry heterogeneity and time-variability in the effects of unconventional monetary policies (UMPs) in advanced economies (AEs) on portfolio inflows to emerging economies (EMEs), with a panel smooth transition regression model. The drivers of the two dimensional nonlinearities are country-specific factors such as the current account, real effective exchange rate deviation from its historical average, and foreign exchange reserves. The elasticity of portfolio inflows to EMEs with respect to a direct quantitative measure of UMP, growth in the Fed's security assets, tends to be higher with a higher current account, higher exchange rate appreciation expectations, and greater foreign exchange reserve holdings, while the results are the opposite with a price measure of UMP, a change in the US 10-year Treasury yield. These results imply that a price UMP shock from news about or impending QE tapering would more adversely affect an EME with a weaker external sector. If QE tapering is actually implemented with clearer signs of economic recovery in AEs, the increase in global liquidity due to AE recoveries will help EMEs muddle relatively easily through the quantitative shock from the reduction in the Fed's security assets.