How can teaching assistants deal with grade disputes? From the answers to this question, it is clear that TAs in the US are usually responsible for grading students' work.
In my country, most of the TAs face the following challenges:


Students confront TAs and attempt to negotiate for extra marks in order to pass, or to improve a grade;

Students confront TAs and attempt to negotiate for extra marks by using a friend's answers as evidence to support their case;

Students inquire about the subtle methods used in grading: the amount of marks awarded for each step, the reason for a decrease of even 0.5 marks, or they ask to see the solution manual, etc.,



And then these conflicts evolve into personal enmities, which may eventually cause the TA serious consequences (a heated confrontation, loss of students' respect, etc.).
The issue is worst if the assignment's answers are quantitative or mathematical. There is no solution manual and sometimes no way to guarantee consistent and fair marking over a great number of student assignments (even for a single particular question).
So I want to know how TAs in the US—or in other countries—avoid these complications. What are the key techniques?
Note: Some say it's a minor issue. No. It is a major issue and often arises with TAs in my country, where the professor is not involved in the distribution or evaluation of grades.
In the United States, the professor responsible for the course should take responsibility for resolving disputes (but not requests for corrections and clarifications).  There is an expectation that they will be heavily involved in grading, even if the bulk of it is done by teaching assistants.
In some cases, the professor may choose not to involve themselves in grading at all, and leave it up to teaching assistants to resolve disputes.  I do not agree with this practice, but if you are stuck with it, you can handle disputes by:

Using a rubric to grade.
Resolving all disputes using the rubric.
Refusing to compare the work of different students.  In the USA, comparing students' papers runs a risk of violating privacy laws.

Ultimately a portion of students will never agree with you about how you grade (they want to learn something different from what you are expected to teach) and this simply must be tolerated.