Those other timelines will continue to exist and the portions of your soul experiencing their existence on those other timelines will continue with that unfolding. What will change is the contribution, if any, of the current incarnation influencing what is going on, on the other timelines energetically. The crosstalk will end in the movement back and forth through time to that portion of the soul in the current incarnation. Upon your death and return to the light, that will end your involvement and influence on those other portions of the soul on the various planes of existence in the parallel timelines still ongoing. When they are completed, the information and the energies will be recorded within the akashic records and are referenceable indefinitely into the future, and will be an influence and factor in all that happens for the ongoing soul journey and future endeavors and adventures by the soul in all that it does.
When you enter into a plane of existence, the energies on record of any prior excursions into that plane of existence will resonate most strongly and there will be an interplay through an awareness and a revisiting of the akashic records for learning, and orientation, and ongoing sources of reference, to gain from prior learning as being one example of the benefits of this process. Anything that happens becomes a record of possibilities and all that is taking place is monitored continually by the Law of Karma to keep things orderly in looking for imbalances and seeking ways to ensure that a rebalancing is done at some point by the soul extensions responsible or participating, as the case might be, as in a perpetrator versus victim scenario where both will become out of balance but may vary in their relative responsibility for making restitution, but both will be influenced and both have an obligation to see to their end of things in the best way they can. This becomes a learning and growth opportunity, both, that will end up enriching all involved.