Using TESS we are doing a systematic study of outbursting AM~CVn systems to place some limits on the current outbursts models. We present the TESS light curve (LC) for 9 AM~CVns showing both superoutbursts (SO) and normal outbursts (NO). The continuous coverage of the outbursts with TESS allows us to place stringent limits on the duration and structures of the SO and the NO. We present evidence that in at least some of the systems enhanced mass transfer (EMT) has to be taken into account to explain the observed LC of the SO and rebrighthening phase after the SO. For others, the colour evolution from simultaneous observations in $g$ and $r$ with ZTF differs from previously reported color evolution of longer period AM~CVns where EMT is responsible for the SO. We also find that due to the lack of sufficiently high cadence coverage many of the duration might have been overestimated in previous ground-based surveys and report the SO duration for 6 AM~CVns. We also found that precursors are a common feature of SO in AM~CVns and are seen in the LC of 5 of the 6 reported SO. Finally with the 10-minute and 2-minute cadence LC from TESS also allowed us to find two new candidates orbital periods of AM~CVns, both of which are in reasonably good agreement with the predictions for their periods based on their past outburst histories.