We study the influence of stratification on stellar turbulent convection near the stellar surface and at various depths by carrying out three-dimensional, high-resolution hydrodynamic simulations with the Anelastic Spherical Harmonic code. Four simulations with different radial-density contrasts corresponding to different aspect ratios for the same underlying 4 Myr, 0.7 M ☉ pre-main-sequence star model are performed. We highlight the existence of giant cells that are embedded in the complex surface convective patterns using a wavelet and time-correlation analysis. Next, we study their properties, such as lifetime, aspect ratio, and spatial extension, in the different models according to the density contrast. We find that these giant cells have a lifetime larger than the stellar period, with a typical longitudinal width of 490 Mm and a latitudinal extension increasing with the radial-density contrast, surpassing 50° in the thickest convective zone. Their rotation rate is much larger than the local differential rotation rate, also increasing with radial-density contrast. However, their spatial coherence as a function of depth decreases with density contrast due to the stronger shear present in these more stratified cases.