Ranma replaces Tenchi.
I do not really see this all that often... A handful of times I have though.
Ranma's strengths and abilities are badly managed when putting them against the strengths and abilities of the Tenchi Muyo cast, making him either too weak or too strong in comparison.
In fairness... it makes a difference first if this is OAV or TIT or Universe... Unless OAV Tenchi and actually manages to go full bore... Ranma can trounce him. With OAV Tenchi going full bore... considering we've seen him split universes and exit black holes... Ranma cannot touch him.
The issue though becomes Ryoko, Kagato/Kain, and the goddesses. As I believe a post manga Ranma could defeat everyone but these.
Once again we have to go through the events of the first and second OVAs (especially the first), and the plot involves little else with the addition of Ranma, beyond Ryoga popping up or being chased by and/or looked for by various people from Ranma 1/2 for the usual reasons.
Generally, I see Ranma's introduction into Tenchi destroy the Tenchi timeline... the few times it does not utterly destroy it, it is often due to external time events still occuring... for example, Ranma being interoduced would change little of the Arrivals of (depending on timeline) Kagato, Kiyone, Seto, Masaki parents, or the hot springs event. None of those would generally be affected by Ranma being introduced.