Control Surface transition with sketch

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Hello,
First post here so apologise if this has been covered before, but my searching has found the answer.
I would like to create T-Spline surfaces but constrained to existing sketches or geometry. By that I mean imagine a cup/mug with a handle. If the point at which the handle leaves the cup was a shape driven by a sketch, could be a perfect circle or something more complicated and same would apply where the handle returns and meets the cup again, but I can manipulate the surface in between. Another example would be a biscuit tin with straight vertical sides that are driven by a sketch (straight lines and raduis's) but I wanted to model a more organic lid bit maintain and control the connection to the side geometry.
Hope those descriptions get across how I would like to control the connection from a geometric shape to an organic surface.
Thanks for any help
Simon