In this talk, I will present the outcome of three-dimensional simulations studying the interaction between a magnetized solar-mass protostar and its surrounding accretion disk. The standard picture of magnetospheric accretion suggests that the disk gas reaches the stellar surface through accretion funnels or curtains, the so-called stable accretion regime. Three-dimensional models are able to capture the intrinsically non-axisymmetric interchange (or magnetized Rayleigh-Taylor) instability that can develop at the magnetospheric boundary. Previous works have shown that this instability results in the formation of equatorial accretion tongues, which penetrate the stellar magnetosphere, further affecting the stellar photometric variability. This is the unstable accretion regime. The critical parameter, which characterises both the accretion state (stable or unstable) and the angular-momentum transport in the star-disk system, is the ratio between the disk truncation radius and the system co-rotation radius (where the disk rotation rate matches the stellar rotation rate). I will present a new scaling that predicts the disk truncation radius from the system global parameters such as the mass accretion rate, stellar mass and radius, magnetic field strength. In addition, I will demonstrate that stable accretion is a key ingredient for a stellar spin-down, with a spin-down timescale of about one Myr and thus, it can explain the observed slow rotation of classical T Tauri stars (i.e., class II low-mass young stellar objects). Finally, I will discuss how the observed variability in T Tauri stars, likely linked (consequence) with the accretion state, can provide insights on the rotational evolution state of the central object (spin-down or spin-up).