Over the last decade, the MOST satellite provided a handful of high-precision light curves of pre-main sequence stars. TW Hya - the closest CTTS to us and accreting disc plasma with a moderate rate of 1e-9 solar mass per year - was observed seven times. It always showed slightly different light variations, either more or less irregular, what may be interpreted that accretion can switch between an unstable and a moderately stable regime. Interestingly, RU Lup having one of the highest known accretion rates (1e-8) always showed irregular behavior typical for unstable accretion, while slowly accreting (1e-11) IM Lup showed regular light variations both in space-based and in long-term ASAS data, what is typical for stable accretion regime. All the above appears to be in agreement with the numerical picture successively developed by Dr. M. Romanova group. Their models predict also waves induced in the disc plasma structure due to interactions with a rotating tilted magnetosphere of a star. In particular, the solution for CTTS with enhanced accretion is one of several possibilities that can be used for interpretation of quasi-periodic light variations arising in the inner disc of FU Ori.