Before revision:  In the data-dominated region, where the number  of different assets in the portfolio is much less than the length  of the available time series, the regularizer plays a negligible role  , while in the (much more frequently occurring in practice) opposite limit, where the samples are comparable or even small compared to the number of different assets, the optimum is almost entirely determined by the regularizer.
After revision:  In the data-dominated region, where the number of different assets in the portfolio is much less than the length of the available time series, the regularizer plays a negligible role , while in the (much more frequently occurring in practice) opposite limit, where the size of samples is comparable to, or even smaller than the number of different assets, the optimum is almost entirely determined by the regularizer.